linear_algebra.affine_space.combination
⟷
Mathlib.LinearAlgebra.AffineSpace.Combination
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(last sync)
The implicitness caused problems in elaboration. In Lean 3 it only amounts to long elaboration times, but in Lean 4 elaboration fails.
@@ -331,6 +331,8 @@ lemma weighted_vsub_const_smul (w : ι → k) (p : ι → P) (c : k) :
s.weighted_vsub p (c • w) = c • s.weighted_vsub p w :=
s.weighted_vsub_of_point_const_smul _ _ _ _
+variables (k)
+
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
the weights. This is intended to be used when the sum of the weights
@@ -346,9 +348,11 @@ def affine_combination (p : ι → P) : (ι → k) →ᵃ[k] P :=
/-- The linear map corresponding to `affine_combination` is
`weighted_vsub`. -/
@[simp] lemma affine_combination_linear (p : ι → P) :
- (s.affine_combination p : (ι → k) →ᵃ[k] P).linear = s.weighted_vsub p :=
+ (s.affine_combination k p).linear = s.weighted_vsub p :=
rfl
+variables {k}
+
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
when that base point will cancel out later); a more typical use case
@@ -357,41 +361,41 @@ point with
`affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one` and
then using `weighted_vsub_of_point_apply`. -/
lemma affine_combination_apply (w : ι → k) (p : ι → P) :
- s.affine_combination p w =
+ s.affine_combination k p w =
s.weighted_vsub_of_point p (classical.choice S.nonempty) w +ᵥ (classical.choice S.nonempty) :=
rfl
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp] lemma affine_combination_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 1) :
- s.affine_combination (λ _, p) w = p :=
+ s.affine_combination k (λ _, p) w = p :=
by rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
lemma affine_combination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
- (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.affine_combination p₁ w₁ = s.affine_combination p₂ w₂ :=
+ (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.affine_combination k p₁ w₁ = s.affine_combination k p₂ w₂ :=
by simp_rw [affine_combination_apply, s.weighted_vsub_of_point_congr hw hp]
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
lemma affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
(h : ∑ i in s, w i = 1) (b : P) :
- s.affine_combination p w = s.weighted_vsub_of_point p b w +ᵥ b :=
+ s.affine_combination k p w = s.weighted_vsub_of_point p b w +ᵥ b :=
s.weighted_vsub_of_point_vadd_eq_of_sum_eq_one w p h _ _
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
lemma weighted_vsub_vadd_affine_combination (w₁ w₂ : ι → k) (p : ι → P) :
- s.weighted_vsub p w₁ +ᵥ s.affine_combination p w₂ = s.affine_combination p (w₁ + w₂) :=
+ s.weighted_vsub p w₁ +ᵥ s.affine_combination k p w₂ = s.affine_combination k p (w₁ + w₂) :=
by rw [←vadd_eq_add, affine_map.map_vadd, affine_combination_linear]
/-- Subtracting two `affine_combination`s. -/
lemma affine_combination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
- s.affine_combination p w₁ -ᵥ s.affine_combination p w₂ = s.weighted_vsub p (w₁ - w₂) :=
+ s.affine_combination k p w₁ -ᵥ s.affine_combination k p w₂ = s.weighted_vsub p (w₁ - w₂) :=
by rw [←affine_map.linear_map_vsub, affine_combination_linear, vsub_eq_sub]
lemma attach_affine_combination_of_injective [decidable_eq P]
(s : finset P) (w : P → k) (f : s → P) (hf : function.injective f) :
- s.attach.affine_combination f (w ∘ f) = (image f univ).affine_combination id w :=
+ s.attach.affine_combination k f (w ∘ f) = (image f univ).affine_combination k id w :=
begin
simp only [affine_combination, weighted_vsub_of_point_apply, id.def, vadd_right_cancel_iff,
function.comp_app, affine_map.coe_mk],
@@ -404,7 +408,7 @@ begin
end
lemma attach_affine_combination_coe (s : finset P) (w : P → k) :
- s.attach.affine_combination (coe : s → P) (w ∘ coe) = s.affine_combination id w :=
+ s.attach.affine_combination k (coe : s → P) (w ∘ coe) = s.affine_combination k id w :=
by classical; rw [attach_affine_combination_of_injective s w (coe : s → P) subtype.coe_injective,
univ_eq_attach, attach_image_coe]
@@ -421,7 +425,7 @@ by simp [s.weighted_vsub_apply, vsub_eq_sub, smul_sub, ← finset.sum_smul, hw]
combinations. -/
@[simp] lemma affine_combination_eq_linear_combination (s : finset ι) (p : ι → V) (w : ι → k)
(hw : ∑ i in s, w i = 1) :
- s.affine_combination p w = ∑ i in s, w i • p i :=
+ s.affine_combination k p w = ∑ i in s, w i • p i :=
by simp [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw 0]
include S
@@ -430,7 +434,7 @@ include S
and has weight 1 and the other points in the set have weight 0. -/
@[simp] lemma affine_combination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i : ι}
(his : i ∈ s) (hwi : w i = 1) (hw0 : ∀ i2 ∈ s, i2 ≠ i → w i2 = 0) :
- s.affine_combination p w = p i :=
+ s.affine_combination k p w = p i :=
begin
have h1 : ∑ i in s, w i = 1 := hwi ▸ sum_eq_single i hw0 (λ h, false.elim (h his)),
rw [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p h1 (p i),
@@ -447,7 +451,7 @@ end
corresponding indicator function and adding points to the set. -/
lemma affine_combination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : finset ι}
(h : s₁ ⊆ s₂) :
- s₁.affine_combination p w = s₂.affine_combination p (set.indicator ↑s₁ w) :=
+ s₁.affine_combination k p w = s₂.affine_combination k p (set.indicator ↑s₁ w) :=
by rw [affine_combination_apply, affine_combination_apply,
weighted_vsub_of_point_indicator_subset _ _ _ h]
@@ -455,13 +459,13 @@ by rw [affine_combination_apply, affine_combination_apply,
affine combination with the same points and weights over the original
`finset`. -/
lemma affine_combination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
- (s₂.map e).affine_combination p w = s₂.affine_combination (p ∘ e) (w ∘ e) :=
+ (s₂.map e).affine_combination k p w = s₂.affine_combination k (p ∘ e) (w ∘ e) :=
by simp_rw [affine_combination_apply, weighted_vsub_of_point_map]
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
lemma sum_smul_vsub_eq_affine_combination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
- ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.affine_combination p₁ w -ᵥ s.affine_combination p₂ w :=
+ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.affine_combination k p₁ w -ᵥ s.affine_combination k p₂ w :=
begin
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right],
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
@@ -471,20 +475,20 @@ end
sum of the weights is 1. -/
lemma sum_smul_vsub_const_eq_affine_combination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
(h : ∑ i in s, w i = 1) :
- ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.affine_combination p₁ w -ᵥ p₂ :=
+ ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.affine_combination k p₁ w -ᵥ p₂ :=
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
lemma sum_smul_const_vsub_eq_vsub_affine_combination (w : ι → k) (p₂ : ι → P) (p₁ : P)
(h : ∑ i in s, w i = 1) :
- ∑ i in s, w i • (p₁ -ᵥ p₂ i) = p₁ -ᵥ s.affine_combination p₂ w :=
+ ∑ i in s, w i • (p₁ -ᵥ p₂ i) = p₁ -ᵥ s.affine_combination k p₂ w :=
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
lemma affine_combination_sdiff_sub [decidable_eq ι] {s₂ : finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) :
- (s \ s₂).affine_combination p w -ᵥ s₂.affine_combination p (-w) = s.weighted_vsub p w :=
+ (s \ s₂).affine_combination k p w -ᵥ s₂.affine_combination k p (-w) = s.weighted_vsub p w :=
begin
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right],
exact s.weighted_vsub_sdiff_sub h _ _
@@ -494,7 +498,7 @@ end
the affine combination of the other points with the given weights. -/
lemma affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
(hw : s.weighted_vsub p w = (0 : V)) {i : ι} [decidable_pred (≠ i)] (his : i ∈ s)
- (hwi : w i = -1) : (s.filter (≠ i)).affine_combination p w = p i :=
+ (hwi : w i = -1) : (s.filter (≠ i)).affine_combination k p w = p i :=
begin
classical,
rw [←@vsub_eq_zero_iff_eq V, ←hw,
@@ -509,15 +513,15 @@ end
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
lemma affine_combination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[decidable_pred pred] :
- (s.subtype pred).affine_combination (λ i, p i) (λ i, w i) =
- (s.filter pred).affine_combination p w :=
+ (s.subtype pred).affine_combination k (λ i, p i) (λ i, w i) =
+ (s.filter pred).affine_combination k p w :=
by rw [affine_combination_apply, affine_combination_apply, weighted_vsub_of_point_subtype_eq_filter]
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
lemma affine_combination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop}
[decidable_pred pred] (h : ∀ i ∈ s, w i ≠ 0 → pred i) :
- (s.filter pred).affine_combination p w = s.affine_combination p w :=
+ (s.filter pred).affine_combination k p w = s.affine_combination k p w :=
by rw [affine_combination_apply, affine_combination_apply,
s.weighted_vsub_of_point_filter_of_ne _ _ _ h]
@@ -575,9 +579,9 @@ subset. -/
lemma eq_affine_combination_subset_iff_eq_affine_combination_subtype {p0 : P} {s : set ι}
{p : ι → P} :
(∃ (fs : finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : ∑ i in fs, w i = 1),
- p0 = fs.affine_combination p w) ↔
+ p0 = fs.affine_combination k p w) ↔
∃ (fs : finset s) (w : s → k) (hw : ∑ i in fs, w i = 1),
- p0 = fs.affine_combination (λ (i : s), p i) w :=
+ p0 = fs.affine_combination k (λ (i : s), p i) w :=
begin
simp_rw [affine_combination_apply, eq_vadd_iff_vsub_eq],
exact eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype
@@ -588,7 +592,7 @@ variables {k V}
/-- Affine maps commute with affine combinations. -/
lemma map_affine_combination {V₂ P₂ : Type*} [add_comm_group V₂] [module k V₂] [affine_space V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.sum w = 1) (f : P →ᵃ[k] P₂) :
- f (s.affine_combination p w) = s.affine_combination (f ∘ p) w :=
+ f (s.affine_combination k p w) = s.affine_combination k (f ∘ p) w :=
begin
have b := classical.choice (infer_instance : affine_space V P).nonempty,
have b₂ := classical.choice (infer_instance : affine_space V₂ P₂).nonempty,
@@ -684,7 +688,7 @@ variables (k)
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp] lemma affine_combination_affine_combination_single_weights [decidable_eq ι] (p : ι → P)
- {i : ι} (hi : i ∈ s) : s.affine_combination p (affine_combination_single_weights k i) = p i :=
+ {i : ι} (hi : i ∈ s) : s.affine_combination k p (affine_combination_single_weights k i) = p i :=
begin
refine s.affine_combination_of_eq_one_of_eq_zero _ _ hi (by simp) _,
rintro j - hj,
@@ -707,7 +711,7 @@ variables {k}
`line_map`. -/
@[simp] lemma affine_combination_affine_combination_line_map_weights [decidable_eq ι] (p : ι → P)
{i j : ι} (hi : i ∈ s) (hj : j ∈ s) (c : k) :
- s.affine_combination p (affine_combination_line_map_weights i j c) =
+ s.affine_combination k p (affine_combination_line_map_weights i j c) =
affine_map.line_map (p i) (p j) c :=
by rw [affine_combination_line_map_weights, ←weighted_vsub_vadd_affine_combination,
weighted_vsub_const_smul, s.affine_combination_affine_combination_single_weights k p hi,
@@ -766,11 +770,11 @@ include V
is intended to be used in the case where the number of points,
converted to `k`, is not zero. -/
def centroid (p : ι → P) : P :=
-s.affine_combination p (s.centroid_weights k)
+s.affine_combination k p (s.centroid_weights k)
/-- The definition of the centroid. -/
lemma centroid_def (p : ι → P) :
- s.centroid k p = s.affine_combination p (s.centroid_weights k) :=
+ s.centroid k p = s.affine_combination k p (s.centroid_weights k) :=
rfl
lemma centroid_univ (s : finset P) :
@@ -865,7 +869,7 @@ include V
/-- The centroid as an affine combination over a `fintype`. -/
lemma centroid_eq_affine_combination_fintype [fintype ι] (p : ι → P) :
- s.centroid k p = univ.affine_combination p (s.centroid_weights_indicator k) :=
+ s.centroid k p = univ.affine_combination k p (s.centroid_weights_indicator k) :=
affine_combination_indicator_subset _ _ (subset_univ _)
/-- An indexed family of points that is injective on the given
@@ -948,7 +952,7 @@ end
nontrivial. -/
lemma affine_combination_mem_affine_span [nontrivial k] {s : finset ι} {w : ι → k}
(h : ∑ i in s, w i = 1) (p : ι → P) :
- s.affine_combination p w ∈ affine_span k (set.range p) :=
+ s.affine_combination k p w ∈ affine_span k (set.range p) :=
begin
classical,
have hnz : ∑ i in s, w i ≠ 0 := h.symm ▸ one_ne_zero,
@@ -957,14 +961,14 @@ begin
let w1 : ι → k := function.update (function.const ι 0) i1 1,
have hw1 : ∑ i in s, w1 i = 1,
{ rw [finset.sum_update_of_mem hi1, finset.sum_const_zero, add_zero] },
- have hw1s : s.affine_combination p w1 = p i1 :=
+ have hw1s : s.affine_combination k p w1 = p i1 :=
s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (function.update_same _ _ _)
(λ _ _ hne, function.update_noteq hne _ _),
- have hv : s.affine_combination p w -ᵥ p i1 ∈ (affine_span k (set.range p)).direction,
+ have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affine_span k (set.range p)).direction,
{ rw [direction_affine_span, ←hw1s, finset.affine_combination_vsub],
apply weighted_vsub_mem_vector_span,
simp [pi.sub_apply, h, hw1] },
- rw ←vsub_vadd (s.affine_combination p w) (p i1),
+ rw ←vsub_vadd (s.affine_combination k p w) (p i1),
exact affine_subspace.vadd_mem_of_mem_direction hv (mem_affine_span k (set.mem_range_self _))
end
@@ -1019,7 +1023,7 @@ variables {k}
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
lemma eq_affine_combination_of_mem_affine_span {p1 : P} {p : ι → P}
(h : p1 ∈ affine_span k (set.range p)) :
- ∃ (s : finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affine_combination p w :=
+ ∃ (s : finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affine_combination k p w :=
begin
classical,
have hn : ((affine_span k (set.range p)) : set P).nonempty := ⟨p1, h⟩,
@@ -1040,7 +1044,7 @@ begin
let w0 : ι → k := function.update (function.const ι 0) i0 1,
have hw0 : ∑ i in s', w0 i = 1,
{ rw [finset.sum_update_of_mem (finset.mem_insert_self _ _), finset.sum_const_zero, add_zero] },
- have hw0s : s'.affine_combination p w0 = p i0 :=
+ have hw0s : s'.affine_combination k p w0 = p i0 :=
s'.affine_combination_of_eq_one_of_eq_zero w0 p
(finset.mem_insert_self _ _)
(function.update_same _ _ _)
@@ -1053,7 +1057,7 @@ end
lemma eq_affine_combination_of_mem_affine_span_of_fintype [fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affine_span k (set.range p)) :
- ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = finset.univ.affine_combination p w :=
+ ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = finset.univ.affine_combination k p w :=
begin
classical,
obtain ⟨s, w, hw, rfl⟩ := eq_affine_combination_of_mem_affine_span h,
@@ -1069,7 +1073,7 @@ if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
lemma mem_affine_span_iff_eq_affine_combination [nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affine_span k (set.range p) ↔
- ∃ (s : finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affine_combination p w :=
+ ∃ (s : finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affine_combination k p w :=
begin
split,
{ exact eq_affine_combination_of_mem_affine_span },
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(no changes)
(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,8 +3,8 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
-import Algebra.Invertible
-import Algebra.IndicatorFunction
+import Algebra.Invertible.Defs
+import Algebra.Function.Indicator
import Algebra.Module.BigOperators
import Data.Fintype.BigOperators
import LinearAlgebra.AffineSpace.AffineMap
@@ -1160,7 +1160,7 @@ theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i j «expr ∈ » s) -/
#print Finset.centroid_eq_centroid_image_of_inj_on /-
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
@@ -1197,8 +1197,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
#print Finset.centroid_eq_of_inj_on_of_image_eq /-
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -1299,7 +1299,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero, sub_self]
use hw
have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
- change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
+ change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
change ∑ i in l.support, l i • _ = _
@@ -1328,12 +1328,12 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
∃ (s : Finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
- rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
+ rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
cases' hn with i0
have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
AffineSubspace.vsub_mem_direction h h0
- rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
+ rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
rcases hd with ⟨s, w, h, hs⟩
let s' := insert i0 s
let w' := Set.indicator (↑s) w
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -550,7 +550,8 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
#print Finset.attach_affineCombination_coe /-
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
- classical
+ classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
+ univ_eq_attach, attach_image_coe]
#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coe
-/
@@ -659,7 +660,14 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
the affine combination of the other points with the given weights. -/
theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
(hw : s.weightedVSub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
- (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by classical
+ (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by
+ classical
+ rw [← @vsub_eq_zero_iff_eq V, ← hw, ← s.affine_combination_sdiff_sub (singleton_subset_iff.2 his),
+ sdiff_singleton_eq_erase, ← filter_ne']
+ congr
+ refine' (affine_combination_of_eq_one_of_eq_zero _ _ _ (mem_singleton_self _) _ _).symm
+ · simp [hwi]
+ · simp
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
-/
@@ -701,7 +709,17 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
v = fs.weightedVSubOfPoint p b w) ↔
∃ (fs : Finset s) (w : s → k) (hw : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
- by classical
+ by
+ classical
+ simp_rw [weighted_vsub_of_point_apply]
+ constructor
+ · rintro ⟨fs, hfs, w, rfl, rfl⟩
+ use fs.subtype s, fun i => w i, sum_subtype_of_mem _ hfs, (sum_subtype_of_mem _ hfs).symm
+ · rintro ⟨fs, w, rfl, rfl⟩
+ refine'
+ ⟨fs.map (Function.Embedding.subtype _), map_subtype_subset _, fun i =>
+ if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
+ simp
#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
-/
@@ -1188,7 +1206,9 @@ have the same centroid. -/
theorem centroid_eq_of_inj_on_of_image_eq {p : ι → P}
(hi : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), p i = p j → i = j) {p₂ : ι₂ → P}
(hi₂ : ∀ (i) (_ : i ∈ s₂) (j) (_ : j ∈ s₂), p₂ i = p₂ j → i = j) (he : p '' ↑s = p₂ '' ↑s₂) :
- s.centroid k p = s₂.centroid k p₂ := by classical
+ s.centroid k p = s₂.centroid k p₂ := by
+ classical rw [s.centroid_eq_centroid_image_of_inj_on k hi rfl,
+ s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eq
-/
@@ -1205,7 +1225,22 @@ variable {ι : Type _}
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in s, w i = 0) (p : ι → P) :
- s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by classical
+ s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
+ classical
+ rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
+ · skip; simp [Finset.eq_empty_of_isEmpty s]
+ · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
+ Finsupp.mem_span_image_iff_total,
+ Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
+ Finset.weightedVSubOfPoint_apply]
+ let w' := Set.indicator (↑s) w
+ have hwx : ∀ i, w' i ≠ 0 → i ∈ s := fun i => Set.mem_of_indicator_ne_zero
+ use Finsupp.onFinset s w' hwx, Set.subset_univ _
+ rw [Finsupp.total_apply, Finsupp.onFinset_sum hwx]
+ · apply Finset.sum_congr rfl
+ intro i hi
+ simp [w', Set.indicator_apply, if_pos hi]
+ · exact fun _ => zero_smul k _
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
-/
@@ -1215,7 +1250,24 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in
nontrivial. -/
theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι → k}
(h : ∑ i in s, w i = 1) (p : ι → P) : s.affineCombination k p w ∈ affineSpan k (Set.range p) :=
- by classical
+ by
+ classical
+ have hnz : ∑ i in s, w i ≠ 0 := h.symm ▸ one_ne_zero
+ have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
+ cases' hn with i1 hi1
+ let w1 : ι → k := Function.update (Function.const ι 0) i1 1
+ have hw1 : ∑ i in s, w1 i = 1 := by
+ rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
+ have hw1s : s.affine_combination k p w1 = p i1 :=
+ s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
+ Function.update_noteq hne _ _
+ have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
+ by
+ rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
+ apply weightedVSub_mem_vectorSpan
+ simp [Pi.sub_apply, h, hw1]
+ rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
+ exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
#align affine_combination_mem_affine_span affineCombination_mem_affineSpan
-/
@@ -1227,7 +1279,41 @@ if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
∃ (s : Finset ι) (w : ι → k) (h : ∑ i in s, w i = 0), v = s.weightedVSub p w :=
- by classical
+ by
+ classical
+ constructor
+ · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩); swap
+ · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
+ Finsupp.mem_span_image_iff_total]
+ rintro ⟨l, hl, hv⟩
+ use insert i0 l.support
+ set w :=
+ (l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
+ hwdef
+ use w
+ have hw : ∑ i in insert i0 l.support, w i = 0 :=
+ by
+ rw [hwdef]
+ simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
+ Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero,
+ Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero, sub_self]
+ use hw
+ have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
+ change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
+ rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
+ Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
+ change ∑ i in l.support, l i • _ = _
+ congr with i
+ by_cases h : i = i0
+ · simp [h]
+ · simp [hwdef, h]
+ · skip
+ rw [Set.range_eq_empty, vectorSpan_empty, Submodule.mem_bot]
+ rintro rfl
+ use∅
+ simp
+ · rintro ⟨s, w, hw, rfl⟩
+ exact weightedVSub_mem_vectorSpan hw p
#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSub
-/
@@ -1241,13 +1327,44 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (s : Finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
classical
+ have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
+ rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
+ cases' hn with i0
+ have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
+ have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
+ AffineSubspace.vsub_mem_direction h h0
+ rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
+ rcases hd with ⟨s, w, h, hs⟩
+ let s' := insert i0 s
+ let w' := Set.indicator (↑s) w
+ have h' : ∑ i in s', w' i = 0 := by
+ rw [← h, Finset.sum_indicator_subset _ (Finset.subset_insert i0 s)]
+ have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
+ by
+ rw [hs]
+ exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
+ let w0 : ι → k := Function.update (Function.const ι 0) i0 1
+ have hw0 : ∑ i in s', w0 i = 1 := by
+ rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
+ have hw0s : s'.affine_combination k p w0 = p i0 :=
+ s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
+ (Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
+ use s', w0 + w'
+ constructor
+ · simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
+ · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
-/
#print eq_affineCombination_of_mem_affineSpan_of_fintype /-
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by classical
+ ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
+ classical
+ obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
+ refine' ⟨(s : Set ι).indicator w, _, Finset.affineCombination_indicator_subset w p s.subset_univ⟩
+ simp only [Finset.mem_coe, Set.indicator_apply, ← hw]
+ rw [Fintype.sum_extend_by_zero s w]
#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintype
-/
@@ -1282,6 +1399,16 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
exact ⟨s, w, s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw (p j)⟩
· rintro ⟨s, w, rfl⟩
classical
+ let w' : ι → k := Function.update w j (1 - (s \ {j}).Sum w)
+ have h₁ : (insert j s).Sum w' = 1 := by
+ by_cases hj : j ∈ s
+ · simp [Finset.sum_update_of_mem hj, Finset.insert_eq_of_mem hj]
+ · simp [w', Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
+ have hww : ∀ i, i ≠ j → w i = w' i := by intro i hij; simp [w', hij]
+ rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
+ s.weighted_vsub_of_point_insert w' p j, ←
+ (insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
+ exact affineCombination_mem_affineSpan h₁ p
#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -550,8 +550,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
#print Finset.attach_affineCombination_coe /-
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
- classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
- univ_eq_attach, attach_image_coe]
+ classical
#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coe
-/
@@ -660,14 +659,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
the affine combination of the other points with the given weights. -/
theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
(hw : s.weightedVSub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
- (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by
- classical
- rw [← @vsub_eq_zero_iff_eq V, ← hw, ← s.affine_combination_sdiff_sub (singleton_subset_iff.2 his),
- sdiff_singleton_eq_erase, ← filter_ne']
- congr
- refine' (affine_combination_of_eq_one_of_eq_zero _ _ _ (mem_singleton_self _) _ _).symm
- · simp [hwi]
- · simp
+ (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by classical
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
-/
@@ -709,17 +701,7 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
v = fs.weightedVSubOfPoint p b w) ↔
∃ (fs : Finset s) (w : s → k) (hw : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
- by
- classical
- simp_rw [weighted_vsub_of_point_apply]
- constructor
- · rintro ⟨fs, hfs, w, rfl, rfl⟩
- use fs.subtype s, fun i => w i, sum_subtype_of_mem _ hfs, (sum_subtype_of_mem _ hfs).symm
- · rintro ⟨fs, w, rfl, rfl⟩
- refine'
- ⟨fs.map (Function.Embedding.subtype _), map_subtype_subset _, fun i =>
- if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
- simp
+ by classical
#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
-/
@@ -1206,9 +1188,7 @@ have the same centroid. -/
theorem centroid_eq_of_inj_on_of_image_eq {p : ι → P}
(hi : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), p i = p j → i = j) {p₂ : ι₂ → P}
(hi₂ : ∀ (i) (_ : i ∈ s₂) (j) (_ : j ∈ s₂), p₂ i = p₂ j → i = j) (he : p '' ↑s = p₂ '' ↑s₂) :
- s.centroid k p = s₂.centroid k p₂ := by
- classical rw [s.centroid_eq_centroid_image_of_inj_on k hi rfl,
- s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
+ s.centroid k p = s₂.centroid k p₂ := by classical
#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eq
-/
@@ -1225,22 +1205,7 @@ variable {ι : Type _}
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in s, w i = 0) (p : ι → P) :
- s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
- classical
- rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
- · skip; simp [Finset.eq_empty_of_isEmpty s]
- · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
- Finsupp.mem_span_image_iff_total,
- Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
- Finset.weightedVSubOfPoint_apply]
- let w' := Set.indicator (↑s) w
- have hwx : ∀ i, w' i ≠ 0 → i ∈ s := fun i => Set.mem_of_indicator_ne_zero
- use Finsupp.onFinset s w' hwx, Set.subset_univ _
- rw [Finsupp.total_apply, Finsupp.onFinset_sum hwx]
- · apply Finset.sum_congr rfl
- intro i hi
- simp [w', Set.indicator_apply, if_pos hi]
- · exact fun _ => zero_smul k _
+ s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by classical
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
-/
@@ -1250,24 +1215,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in
nontrivial. -/
theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι → k}
(h : ∑ i in s, w i = 1) (p : ι → P) : s.affineCombination k p w ∈ affineSpan k (Set.range p) :=
- by
- classical
- have hnz : ∑ i in s, w i ≠ 0 := h.symm ▸ one_ne_zero
- have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
- cases' hn with i1 hi1
- let w1 : ι → k := Function.update (Function.const ι 0) i1 1
- have hw1 : ∑ i in s, w1 i = 1 := by
- rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
- have hw1s : s.affine_combination k p w1 = p i1 :=
- s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
- Function.update_noteq hne _ _
- have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
- by
- rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
- apply weightedVSub_mem_vectorSpan
- simp [Pi.sub_apply, h, hw1]
- rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
- exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
+ by classical
#align affine_combination_mem_affine_span affineCombination_mem_affineSpan
-/
@@ -1279,41 +1227,7 @@ if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
∃ (s : Finset ι) (w : ι → k) (h : ∑ i in s, w i = 0), v = s.weightedVSub p w :=
- by
- classical
- constructor
- · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩); swap
- · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
- Finsupp.mem_span_image_iff_total]
- rintro ⟨l, hl, hv⟩
- use insert i0 l.support
- set w :=
- (l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
- hwdef
- use w
- have hw : ∑ i in insert i0 l.support, w i = 0 :=
- by
- rw [hwdef]
- simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
- Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero,
- Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero, sub_self]
- use hw
- have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
- change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
- rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
- Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
- change ∑ i in l.support, l i • _ = _
- congr with i
- by_cases h : i = i0
- · simp [h]
- · simp [hwdef, h]
- · skip
- rw [Set.range_eq_empty, vectorSpan_empty, Submodule.mem_bot]
- rintro rfl
- use∅
- simp
- · rintro ⟨s, w, hw, rfl⟩
- exact weightedVSub_mem_vectorSpan hw p
+ by classical
#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSub
-/
@@ -1327,44 +1241,13 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (s : Finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
classical
- have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
- rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
- cases' hn with i0
- have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
- have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
- AffineSubspace.vsub_mem_direction h h0
- rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
- rcases hd with ⟨s, w, h, hs⟩
- let s' := insert i0 s
- let w' := Set.indicator (↑s) w
- have h' : ∑ i in s', w' i = 0 := by
- rw [← h, Finset.sum_indicator_subset _ (Finset.subset_insert i0 s)]
- have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
- by
- rw [hs]
- exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
- let w0 : ι → k := Function.update (Function.const ι 0) i0 1
- have hw0 : ∑ i in s', w0 i = 1 := by
- rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
- have hw0s : s'.affine_combination k p w0 = p i0 :=
- s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
- (Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
- use s', w0 + w'
- constructor
- · simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
- · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
-/
#print eq_affineCombination_of_mem_affineSpan_of_fintype /-
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
- classical
- obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
- refine' ⟨(s : Set ι).indicator w, _, Finset.affineCombination_indicator_subset w p s.subset_univ⟩
- simp only [Finset.mem_coe, Set.indicator_apply, ← hw]
- rw [Fintype.sum_extend_by_zero s w]
+ ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by classical
#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintype
-/
@@ -1399,16 +1282,6 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
exact ⟨s, w, s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw (p j)⟩
· rintro ⟨s, w, rfl⟩
classical
- let w' : ι → k := Function.update w j (1 - (s \ {j}).Sum w)
- have h₁ : (insert j s).Sum w' = 1 := by
- by_cases hj : j ∈ s
- · simp [Finset.sum_update_of_mem hj, Finset.insert_eq_of_mem hj]
- · simp [w', Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
- have hww : ∀ i, i ≠ j → w i = w' i := by intro i hij; simp [w', hij]
- rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
- s.weighted_vsub_of_point_insert w' p j, ←
- (insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
- exact affineCombination_mem_affineSpan h₁ p
#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -196,7 +196,8 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
by
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply]
exact
- Set.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
+ Finset.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i =>
+ zero_smul k _
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
-/
@@ -1113,7 +1114,7 @@ theorem centroidWeightsIndicator_def :
/-- The sum of the weights for the centroid indexed by a `fintype`. -/
theorem sum_centroidWeightsIndicator [Fintype ι] :
∑ i, s.centroidWeightsIndicator k i = ∑ i in s, s.centroidWeights k i :=
- (Set.sum_indicator_subset _ (subset_univ _)).symm
+ (Finset.sum_indicator_subset _ (subset_univ _)).symm
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
-/
@@ -1337,7 +1338,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
let s' := insert i0 s
let w' := Set.indicator (↑s) w
have h' : ∑ i in s', w' i = 0 := by
- rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
+ rw [← h, Finset.sum_indicator_subset _ (Finset.subset_insert i0 s)]
have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
by
rw [hs]
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -776,7 +776,7 @@ theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k
s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w (f ∘ p) hw b₂, ←
s.weighted_vsub_of_point_vadd_eq_of_sum_eq_one w (f ∘ p) hw (f b) b₂]
simp only [weighted_vsub_of_point_apply, RingHom.id_apply, AffineMap.map_vadd,
- LinearMap.map_smulₛₗ, AffineMap.linearMap_vsub, LinearMap.map_sum]
+ LinearMap.map_smulₛₗ, AffineMap.linearMap_vsub, map_sum]
#align finset.map_affine_combination Finset.map_affineCombination
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,14 +3,14 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
-import Mathbin.Algebra.Invertible
-import Mathbin.Algebra.IndicatorFunction
-import Mathbin.Algebra.Module.BigOperators
-import Mathbin.Data.Fintype.BigOperators
-import Mathbin.LinearAlgebra.AffineSpace.AffineMap
-import Mathbin.LinearAlgebra.AffineSpace.AffineSubspace
-import Mathbin.LinearAlgebra.Finsupp
-import Mathbin.Tactic.FinCases
+import Algebra.Invertible
+import Algebra.IndicatorFunction
+import Algebra.Module.BigOperators
+import Data.Fintype.BigOperators
+import LinearAlgebra.AffineSpace.AffineMap
+import LinearAlgebra.AffineSpace.AffineSubspace
+import LinearAlgebra.Finsupp
+import Tactic.FinCases
#align_import linear_algebra.affine_space.combination from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
@@ -1159,7 +1159,7 @@ theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
#print Finset.centroid_eq_centroid_image_of_inj_on /-
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
@@ -1196,8 +1196,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
#print Finset.centroid_eq_of_inj_on_of_image_eq /-
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -1185,7 +1185,7 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
· rintro ⟨i, _, rfl⟩
exact (hf' i).1
· intro hx
- use ⟨p x, hps.symm ▸ Set.mem_image_of_mem _ hx⟩, mem_univ _
+ use⟨p x, hps.symm ▸ Set.mem_image_of_mem _ hx⟩, mem_univ _
refine' hi _ (hf' _).1 _ hx _
rw [(hf' _).2]
rfl
@@ -1309,7 +1309,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
· skip
rw [Set.range_eq_empty, vectorSpan_empty, Submodule.mem_bot]
rintro rfl
- use ∅
+ use∅
simp
· rintro ⟨s, w, hw, rfl⟩
exact weightedVSub_mem_vectorSpan hw p
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Invertible
import Mathbin.Algebra.IndicatorFunction
@@ -17,6 +12,8 @@ import Mathbin.LinearAlgebra.AffineSpace.AffineSubspace
import Mathbin.LinearAlgebra.Finsupp
import Mathbin.Tactic.FinCases
+#align_import linear_algebra.affine_space.combination from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
/-!
# Affine combinations of points
@@ -1162,7 +1159,7 @@ theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
#print Finset.centroid_eq_centroid_image_of_inj_on /-
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
@@ -1199,8 +1196,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
#print Finset.centroid_eq_of_inj_on_of_image_eq /-
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -56,15 +56,15 @@ open scoped BigOperators Affine
namespace Finset
+#print Finset.univ_fin2 /-
theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} := by ext x; fin_cases x <;> simp
#align finset.univ_fin2 Finset.univ_fin2
+-/
variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
variable [S : affine_space V P]
-include S
-
variable {ι : Type _} (s : Finset ι)
variable {ι₂ : Type _} (s₂ : Finset ι₂)
@@ -81,19 +81,24 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
#align finset.weighted_vsub_of_point Finset.weightedVSubOfPoint
-/
+#print Finset.weightedVSubOfPoint_apply /-
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
s.weightedVSubOfPoint p b w = ∑ i in s, w i • (p i -ᵥ b) := by
simp [weighted_vsub_of_point, LinearMap.sum_apply]
#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_apply
+-/
+#print Finset.weightedVSubOfPoint_apply_const /-
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
s.weightedVSubOfPoint (fun _ => p) b w = (∑ i in s, w i) • (p -ᵥ b) := by
rw [weighted_vsub_of_point_apply, sum_smul]
#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_const
+-/
+#print Finset.weightedVSubOfPoint_congr /-
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
@@ -104,7 +109,9 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
convert sum_congr rfl fun i hi => _
rw [hw i hi, hp i hi]
#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congr
+-/
+#print Finset.weightedVSubOfPoint_eq_of_weights_eq /-
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂ : ι → k)
@@ -118,7 +125,9 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
· simp [h]
· simp [hw i h]
#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eq
+-/
+#print Finset.weightedVSubOfPoint_eq_of_sum_eq_zero /-
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 0)
@@ -133,7 +142,9 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
rw [← smul_sub, vsub_sub_vsub_cancel_left]
rw [← sum_smul, h, zero_smul]
#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zero
+-/
+#print Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one /-
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 1)
@@ -151,7 +162,9 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
rw [← smul_sub, vsub_sub_vsub_cancel_left]
rw [← sum_smul, h, one_smul, vsub_add_vsub_cancel, vsub_self]
#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one
+-/
+#print Finset.weightedVSubOfPoint_erase /-
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@[simp]
@@ -162,7 +175,9 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
apply sum_erase
rw [vsub_self, smul_zero]
#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_erase
+-/
+#print Finset.weightedVSubOfPoint_insert /-
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@[simp]
@@ -173,7 +188,9 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
apply sum_insert_zero
rw [vsub_self, smul_zero]
#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insert
+-/
+#print Finset.weightedVSubOfPoint_indicator_subset /-
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b : P) {s₁ s₂ : Finset ι}
@@ -184,7 +201,9 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
exact
Set.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
+-/
+#print Finset.weightedVSubOfPoint_map /-
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
`finset`. -/
@@ -194,7 +213,9 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
simp_rw [weighted_vsub_of_point_apply]
exact Finset.sum_map _ _ _
#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_map
+-/
+#print Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub /-
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι → P) (b : P) :
@@ -202,21 +223,27 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
by
simp_rw [weighted_vsub_of_point_apply, ← sum_sub_distrib, ← smul_sub, vsub_sub_vsub_cancel_right]
#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub
+-/
+#print Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub /-
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι → P) (p₂ b : P) :
∑ i in s, w i • (p₁ i -ᵥ p₂) = s.weightedVSubOfPoint p₁ b w - (∑ i in s, w i) • (p₂ -ᵥ b) := by
rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub
+-/
+#print Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint /-
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι → P) (p₁ b : P) :
∑ i in s, w i • (p₁ -ᵥ p₂ i) = (∑ i in s, w i) • (p₁ -ᵥ b) - s.weightedVSubOfPoint p₂ b w := by
rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
+-/
+#print Finset.weightedVSubOfPoint_sdiff /-
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
@@ -224,7 +251,9 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
s.weightedVSubOfPoint p b w :=
by simp_rw [weighted_vsub_of_point_apply, sum_sdiff h]
#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiff
+-/
+#print Finset.weightedVSubOfPoint_sdiff_sub /-
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
@@ -232,7 +261,9 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
s.weightedVSubOfPoint p b w :=
by rw [map_neg, sub_neg_eq_add, s.weighted_vsub_of_point_sdiff h]
#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_sub
+-/
+#print Finset.weightedVSubOfPoint_subtype_eq_filter /-
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -240,7 +271,9 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
(s.filterₓ pred).weightedVSubOfPoint p b w :=
by rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← sum_subtype_eq_sum_filter]
#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filter
+-/
+#print Finset.weightedVSubOfPoint_filter_of_ne /-
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {pred : ι → Prop}
@@ -253,13 +286,16 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
intro hw
simpa [hw] using hne
#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_ne
+-/
+#print Finset.weightedVSubOfPoint_const_smul /-
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
theorem weightedVSubOfPoint_const_smul (w : ι → k) (p : ι → P) (b : P) (c : k) :
s.weightedVSubOfPoint p b (c • w) = c • s.weightedVSubOfPoint p b w := by
simp_rw [weighted_vsub_of_point_apply, smul_sum, Pi.smul_apply, smul_smul, smul_eq_mul]
#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smul
+-/
#print Finset.weightedVSub /-
/-- A weighted sum of the results of subtracting a default base point
@@ -271,6 +307,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
#align finset.weighted_vsub Finset.weightedVSub
-/
+#print Finset.weightedVSub_apply /-
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
that base point will cancel out later); a more typical use case for
@@ -281,14 +318,18 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
s.weightedVSub p w = ∑ i in s, w i • (p i -ᵥ Classical.choice S.Nonempty) := by
simp [weighted_vsub, LinearMap.sum_apply]
#align finset.weighted_vsub_apply Finset.weightedVSub_apply
+-/
+#print Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero /-
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
(h : ∑ i in s, w i = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
s.weightedVSubOfPoint_eq_of_sum_eq_zero w p h _ _
#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
+-/
+#print Finset.weightedVSub_apply_const /-
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@[simp]
@@ -296,27 +337,35 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 0
s.weightedVSub (fun _ => p) w = 0 := by
rw [weighted_vsub, weighted_vsub_of_point_apply_const, h, zero_smul]
#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_const
+-/
+#print Finset.weightedVSub_empty /-
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).weightedVSub p w = (0 : V) := by
simp [weighted_vsub_apply]
#align finset.weighted_vsub_empty Finset.weightedVSub_empty
+-/
+#print Finset.weightedVSub_congr /-
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
(hp : ∀ i ∈ s, p₁ i = p₂ i) : s.weightedVSub p₁ w₁ = s.weightedVSub p₂ w₂ :=
s.weightedVSubOfPoint_congr hw hp _
#align finset.weighted_vsub_congr Finset.weightedVSub_congr
+-/
+#print Finset.weightedVSub_indicator_subset /-
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι} (h : s₁ ⊆ s₂) :
s₁.weightedVSub p w = s₂.weightedVSub p (Set.indicator (↑s₁) w) :=
weightedVSubOfPoint_indicator_subset _ _ _ h
#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subset
+-/
+#print Finset.weightedVSub_map /-
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
original `finset`. -/
@@ -324,40 +373,52 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
(s₂.map e).weightedVSub p w = s₂.weightedVSub (p ∘ e) (w ∘ e) :=
s₂.weightedVSubOfPoint_map _ _ _ _
#align finset.weighted_vsub_map Finset.weightedVSub_map
+-/
+#print Finset.sum_smul_vsub_eq_weightedVSub_sub /-
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P) :
∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.weightedVSub p₁ w - s.weightedVSub p₂ w :=
s.sum_smul_vsub_eq_weightedVSubOfPoint_sub _ _ _ _
#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_sub
+-/
+#print Finset.sum_smul_vsub_const_eq_weightedVSub /-
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p₂ : P)
(h : ∑ i in s, w i = 0) : ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.weightedVSub p₁ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, sub_zero]
#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
+-/
+#print Finset.sum_smul_const_vsub_eq_neg_weightedVSub /-
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P) (p₁ : P)
(h : ∑ i in s, w i = 0) : ∑ i in s, w i • (p₁ -ᵥ p₂ i) = -s.weightedVSub p₂ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, zero_sub]
#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
+-/
+#print Finset.weightedVSub_sdiff /-
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
(s \ s₂).weightedVSub p w + s₂.weightedVSub p w = s.weightedVSub p w :=
s.weightedVSubOfPoint_sdiff h _ _ _
#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiff
+-/
+#print Finset.weightedVSub_sdiff_sub /-
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) : (s \ s₂).weightedVSub p w - s₂.weightedVSub p (-w) = s.weightedVSub p w :=
s.weightedVSubOfPoint_sdiff_sub h _ _ _
#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_sub
+-/
+#print Finset.weightedVSub_subtype_eq_filter /-
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -365,22 +426,28 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
(s.filterₓ pred).weightedVSub p w :=
s.weightedVSubOfPoint_subtype_eq_filter _ _ _ _
#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filter
+-/
+#print Finset.weightedVSub_filter_of_ne /-
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop} [DecidablePred pred]
(h : ∀ i ∈ s, w i ≠ 0 → pred i) : (s.filterₓ pred).weightedVSub p w = s.weightedVSub p w :=
s.weightedVSubOfPoint_filter_of_ne _ _ _ h
#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_ne
+-/
+#print Finset.weightedVSub_const_smul /-
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
s.weightedVSub p (c • w) = c • s.weightedVSub p w :=
s.weightedVSubOfPoint_const_smul _ _ _ _
#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smul
+-/
variable (k)
+#print Finset.affineCombination /-
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
the weights. This is intended to be used when the sum of the weights
@@ -393,7 +460,9 @@ def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
linear := s.weightedVSub p
map_vadd' w₁ w₂ := by simp_rw [vadd_vadd, weighted_vsub, vadd_eq_add, LinearMap.map_add]
#align finset.affine_combination Finset.affineCombination
+-/
+#print Finset.affineCombination_linear /-
/-- The linear map corresponding to `affine_combination` is
`weighted_vsub`. -/
@[simp]
@@ -401,9 +470,11 @@ theorem affineCombination_linear (p : ι → P) :
(s.affineCombination k p).linear = s.weightedVSub p :=
rfl
#align finset.affine_combination_linear Finset.affineCombination_linear
+-/
variable {k}
+#print Finset.affineCombination_apply /-
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
when that base point will cancel out later); a more typical use case
@@ -416,21 +487,27 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
s.weightedVSubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty :=
rfl
#align finset.affine_combination_apply Finset.affineCombination_apply
+-/
+#print Finset.affineCombination_apply_const /-
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
theorem affineCombination_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 1) :
s.affineCombination k (fun _ => p) w = p := by
rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
+-/
+#print Finset.affineCombination_congr /-
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
(hp : ∀ i ∈ s, p₁ i = p₂ i) : s.affineCombination k p₁ w₁ = s.affineCombination k p₂ w₂ := by
simp_rw [affine_combination_apply, s.weighted_vsub_of_point_congr hw hp]
#align finset.affine_combination_congr Finset.affineCombination_congr
+-/
+#print Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one /-
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
@@ -438,19 +515,25 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
s.affineCombination k p w = s.weightedVSubOfPoint p b w +ᵥ b :=
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
+-/
+#print Finset.weightedVSub_vadd_affineCombination /-
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
s.weightedVSub p w₁ +ᵥ s.affineCombination k p w₂ = s.affineCombination k p (w₁ + w₂) := by
rw [← vadd_eq_add, AffineMap.map_vadd, affine_combination_linear]
#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombination
+-/
+#print Finset.affineCombination_vsub /-
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
s.affineCombination k p w₁ -ᵥ s.affineCombination k p w₂ = s.weightedVSub p (w₁ - w₂) := by
rw [← AffineMap.linearMap_vsub, affine_combination_linear, vsub_eq_sub]
#align finset.affine_combination_vsub Finset.affineCombination_vsub
+-/
+#print Finset.attach_affineCombination_of_injective /-
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w :=
@@ -464,15 +547,17 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
rw [hgf, sum_image]
exact fun _ _ _ _ hxy => hf hxy
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
+-/
+#print Finset.attach_affineCombination_coe /-
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
univ_eq_attach, attach_image_coe]
#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coe
+-/
-omit S
-
+#print Finset.weightedVSub_eq_linear_combination /-
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@[simp]
@@ -480,7 +565,9 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
(hw : s.Sum w = 0) : s.weightedVSub p w = ∑ i in s, w i • p i := by
simp [s.weighted_vsub_apply, vsub_eq_sub, smul_sub, ← Finset.sum_smul, hw]
#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combination
+-/
+#print Finset.affineCombination_eq_linear_combination /-
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@[simp]
@@ -488,9 +575,9 @@ theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (
(hw : ∑ i in s, w i = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
simp [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw 0]
#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combination
+-/
-include S
-
+#print Finset.affineCombination_of_eq_one_of_eq_zero /-
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@[simp]
@@ -507,7 +594,9 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
· simp [h]
· simp [hw0 i2 hi2 h]
#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zero
+-/
+#print Finset.affineCombination_indicator_subset /-
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι}
@@ -516,7 +605,9 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
rw [affine_combination_apply, affine_combination_apply,
weighted_vsub_of_point_indicator_subset _ _ _ h]
#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subset
+-/
+#print Finset.affineCombination_map /-
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
`finset`. -/
@@ -524,7 +615,9 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
(s₂.map e).affineCombination k p w = s₂.affineCombination k (p ∘ e) (w ∘ e) := by
simp_rw [affine_combination_apply, weighted_vsub_of_point_map]
#align finset.affine_combination_map Finset.affineCombination_map
+-/
+#print Finset.sum_smul_vsub_eq_affineCombination_vsub /-
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
@@ -533,21 +626,27 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsub
+-/
+#print Finset.sum_smul_vsub_const_eq_affineCombination_vsub /-
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
(h : ∑ i in s, w i = 1) : ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.affineCombination k p₁ w -ᵥ p₂ := by
rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
+-/
+#print Finset.sum_smul_const_vsub_eq_vsub_affineCombination /-
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
(h : ∑ i in s, w i = 1) : ∑ i in s, w i • (p₁ -ᵥ p₂ i) = p₁ -ᵥ s.affineCombination k p₂ w := by
rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
+-/
+#print Finset.affineCombination_sdiff_sub /-
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) :
@@ -556,7 +655,9 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.weighted_vsub_sdiff_sub h _ _
#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_sub
+-/
+#print Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one /-
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
@@ -570,7 +671,9 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
· simp [hwi]
· simp
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
+-/
+#print Finset.affineCombination_subtype_eq_filter /-
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -579,7 +682,9 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
by
rw [affine_combination_apply, affine_combination_apply, weighted_vsub_of_point_subtype_eq_filter]
#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filter
+-/
+#print Finset.affineCombination_filter_of_ne /-
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop}
@@ -588,9 +693,11 @@ theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι
rw [affine_combination_apply, affine_combination_apply,
s.weighted_vsub_of_point_filter_of_ne _ _ _ h]
#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_ne
+-/
variable {V}
+#print Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype /-
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
`weighted_vsub_of_point` using a `finset` lying within that subset and
@@ -616,9 +723,11 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
simp
#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
+-/
variable (k)
+#print Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype /-
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
a `finset` lying within that subset and with sum of weights 0 if and
@@ -632,9 +741,11 @@ theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι}
v = fs.weightedVSub (fun i : s => p i) w :=
eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
+-/
variable (V)
+#print Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype /-
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
`affine_combination` using a `finset` lying within that subset and
@@ -652,9 +763,11 @@ theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s
simp_rw [affine_combination_apply, eq_vadd_iff_vsub_eq]
exact eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype
#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype
+-/
variable {k V}
+#print Finset.map_affineCombination /-
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.Sum w = 1) (f : P →ᵃ[k] P₂) :
@@ -668,11 +781,10 @@ theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k
simp only [weighted_vsub_of_point_apply, RingHom.id_apply, AffineMap.map_vadd,
LinearMap.map_smulₛₗ, AffineMap.linearMap_vsub, LinearMap.map_sum]
#align finset.map_affine_combination Finset.map_affineCombination
+-/
variable (k)
-omit S
-
#print Finset.affineCombinationSingleWeights /-
/-- Weights for expressing a single point as an affine combination. -/
def affineCombinationSingleWeights [DecidableEq ι] (i : ι) : ι → k :=
@@ -680,16 +792,21 @@ def affineCombinationSingleWeights [DecidableEq ι] (i : ι) : ι → k :=
#align finset.affine_combination_single_weights Finset.affineCombinationSingleWeights
-/
+#print Finset.affineCombinationSingleWeights_apply_self /-
@[simp]
theorem affineCombinationSingleWeights_apply_self [DecidableEq ι] (i : ι) :
affineCombinationSingleWeights k i i = 1 := by simp [affine_combination_single_weights]
#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_self
+-/
+#print Finset.affineCombinationSingleWeights_apply_of_ne /-
@[simp]
theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (h : j ≠ i) :
affineCombinationSingleWeights k i j = 0 := by simp [affine_combination_single_weights, h]
#align finset.affine_combination_single_weights_apply_of_ne Finset.affineCombinationSingleWeights_apply_of_ne
+-/
+#print Finset.sum_affineCombinationSingleWeights /-
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
∑ j in s, affineCombinationSingleWeights k i j = 1 :=
@@ -697,6 +814,7 @@ theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈
rw [← affine_combination_single_weights_apply_self k i]
exact sum_eq_single_of_mem i h fun j _ hj => affine_combination_single_weights_apply_of_ne k hj
#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeights
+-/
#print Finset.weightedVSubVSubWeights /-
/-- Weights for expressing the subtraction of two points as a `weighted_vsub`. -/
@@ -705,26 +823,35 @@ def weightedVSubVSubWeights [DecidableEq ι] (i j : ι) : ι → k :=
#align finset.weighted_vsub_vsub_weights Finset.weightedVSubVSubWeights
-/
+#print Finset.weightedVSubVSubWeights_self /-
@[simp]
theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSubWeights k i i = 0 :=
by simp [weighted_vsub_vsub_weights]
#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_self
+-/
+#print Finset.weightedVSubVSubWeights_apply_left /-
@[simp]
theorem weightedVSubVSubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) :
weightedVSubVSubWeights k i j i = 1 := by simp [weighted_vsub_vsub_weights, h]
#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_left
+-/
+#print Finset.weightedVSubVSubWeights_apply_right /-
@[simp]
theorem weightedVSubVSubWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) :
weightedVSubVSubWeights k i j j = -1 := by simp [weighted_vsub_vsub_weights, h.symm]
#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_right
+-/
+#print Finset.weightedVSubVSubWeights_apply_of_ne /-
@[simp]
theorem weightedVSubVSubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i) (hj : t ≠ j) :
weightedVSubVSubWeights k i j t = 0 := by simp [weighted_vsub_vsub_weights, hi, hj]
#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVSubVSubWeights_apply_of_ne
+-/
+#print Finset.sum_weightedVSubVSubWeights /-
@[simp]
theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
∑ t in s, weightedVSubVSubWeights k i j t = 0 :=
@@ -732,6 +859,7 @@ theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (
simp_rw [weighted_vsub_vsub_weights, Pi.sub_apply, sum_sub_distrib]
simp [hi, hj]
#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVSubVSubWeights
+-/
variable {k}
@@ -750,11 +878,13 @@ theorem affineCombinationLineMapWeights_self [DecidableEq ι] (i : ι) (c : k) :
#align finset.affine_combination_line_map_weights_self Finset.affineCombinationLineMapWeights_self
-/
+#print Finset.affineCombinationLineMapWeights_apply_left /-
@[simp]
theorem affineCombinationLineMapWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) (c : k) :
affineCombinationLineMapWeights i j c i = 1 - c := by
simp [affine_combination_line_map_weights, h.symm, sub_eq_neg_add]
#align finset.affine_combination_line_map_weights_apply_left Finset.affineCombinationLineMapWeights_apply_left
+-/
#print Finset.affineCombinationLineMapWeights_apply_right /-
@[simp]
@@ -764,12 +894,15 @@ theorem affineCombinationLineMapWeights_apply_right [DecidableEq ι] {i j : ι}
#align finset.affine_combination_line_map_weights_apply_right Finset.affineCombinationLineMapWeights_apply_right
-/
+#print Finset.affineCombinationLineMapWeights_apply_of_ne /-
@[simp]
theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i)
(hj : t ≠ j) (c : k) : affineCombinationLineMapWeights i j c t = 0 := by
simp [affine_combination_line_map_weights, hi, hj]
#align finset.affine_combination_line_map_weights_apply_of_ne Finset.affineCombinationLineMapWeights_apply_of_ne
+-/
+#print Finset.sum_affineCombinationLineMapWeights /-
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
(c : k) : ∑ t in s, affineCombinationLineMapWeights i j c t = 1 :=
@@ -777,11 +910,11 @@ theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i
simp_rw [affine_combination_line_map_weights, Pi.add_apply, sum_add_distrib]
simp [hi, hj, ← mul_sum]
#align finset.sum_affine_combination_line_map_weights Finset.sum_affineCombinationLineMapWeights
-
-include S
+-/
variable (k)
+#print Finset.affineCombination_affineCombinationSingleWeights /-
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p : ι → P) {i : ι}
@@ -791,7 +924,9 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
rintro j - hj
simp [hj]
#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeights
+-/
+#print Finset.weightedVSub_weightedVSubVSubWeights /-
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@[simp]
@@ -801,9 +936,11 @@ theorem weightedVSub_weightedVSubVSubWeights [DecidableEq ι] (p : ι → P) {i
s.affine_combination_affine_combination_single_weights k p hi,
s.affine_combination_affine_combination_single_weights k p hj]
#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeights
+-/
variable {k}
+#print Finset.affineCombination_affineCombinationLineMapWeights /-
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@[simp]
@@ -816,6 +953,7 @@ theorem affineCombination_affineCombinationLineMapWeights [DecidableEq ι] (p :
weighted_vsub_const_smul, s.affine_combination_affine_combination_single_weights k p hi,
s.weighted_vsub_weighted_vsub_vsub_weights k p hj hi, AffineMap.lineMap_apply]
#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeights
+-/
end Finset
@@ -832,48 +970,58 @@ def centroidWeights : ι → k :=
#align finset.centroid_weights Finset.centroidWeights
-/
+#print Finset.centroidWeights_apply /-
/-- `centroid_weights` at any point. -/
@[simp]
theorem centroidWeights_apply (i : ι) : s.centroidWeights k i = (card s : k)⁻¹ :=
rfl
#align finset.centroid_weights_apply Finset.centroidWeights_apply
+-/
+#print Finset.centroidWeights_eq_const /-
/-- `centroid_weights` equals a constant function. -/
theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card s : k)⁻¹ :=
rfl
#align finset.centroid_weights_eq_const Finset.centroidWeights_eq_const
+-/
variable {k}
+#print Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero /-
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0) :
∑ i in s, s.centroidWeights k i = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero
+-/
variable (k)
+#print Finset.sum_centroidWeights_eq_one_of_card_ne_zero /-
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠ 0) :
∑ i in s, s.centroidWeights k i = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zero
+-/
+#print Finset.sum_centroidWeights_eq_one_of_nonempty /-
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (ne_of_gt (card_pos.2 h))
#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonempty
+-/
+#print Finset.sum_centroidWeights_eq_one_of_card_eq_add_one /-
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h : card s = n + 1) :
∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (h.symm ▸ Nat.succ_ne_zero n)
#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_one
-
-include V
+-/
#print Finset.centroid /-
/-- The centroid of some points. Although defined for any `s`, this
@@ -884,21 +1032,28 @@ def centroid (p : ι → P) : P :=
#align finset.centroid Finset.centroid
-/
+#print Finset.centroid_def /-
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
rfl
#align finset.centroid_def Finset.centroid_def
+-/
+#print Finset.centroid_univ /-
theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id := by
rw [centroid, centroid, ← s.attach_affine_combination_coe]; congr; ext; simp
#align finset.centroid_univ Finset.centroid_univ
+-/
+#print Finset.centroid_singleton /-
/-- The centroid of a single point. -/
@[simp]
theorem centroid_singleton (p : ι → P) (i : ι) : ({i} : Finset ι).centroid k p = p i := by
simp [centroid_def, affine_combination_apply]
#align finset.centroid_singleton Finset.centroid_singleton
+-/
+#print Finset.centroid_pair /-
/-- The centroid of two points, expressed directly as adding a vector
to a point. -/
theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁ i₂ : ι) :
@@ -916,7 +1071,9 @@ theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁
(sum_centroid_weights_eq_one_of_cast_card_ne_zero _ hc) (p i₁)]
simp [h]
#align finset.centroid_pair Finset.centroid_pair
+-/
+#print Finset.centroid_pair_fin /-
/-- The centroid of two points indexed by `fin 2`, expressed directly
as adding a vector to the first point. -/
theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
@@ -925,14 +1082,15 @@ theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
rw [univ_fin2]
convert centroid_pair k p 0 1
#align finset.centroid_pair_fin Finset.centroid_pair_fin
+-/
+#print Finset.centroid_map /-
/-- A centroid, over the image of an embedding, equals a centroid with
the same points and weights over the original `finset`. -/
theorem centroid_map (e : ι₂ ↪ ι) (p : ι → P) : (s₂.map e).centroid k p = s₂.centroid k (p ∘ e) :=
by simp [centroid_def, affine_combination_map, centroid_weights]
#align finset.centroid_map Finset.centroid_map
-
-omit V
+-/
#print Finset.centroidWeightsIndicator /-
/-- `centroid_weights` gives the weights for the centroid as a
@@ -946,11 +1104,13 @@ def centroidWeightsIndicator : ι → k :=
#align finset.centroid_weights_indicator Finset.centroidWeightsIndicator
-/
+#print Finset.centroidWeightsIndicator_def /-
/-- The definition of `centroid_weights_indicator`. -/
theorem centroidWeightsIndicator_def :
s.centroidWeightsIndicator k = Set.indicator (↑s) (s.centroidWeights k) :=
rfl
#align finset.centroid_weights_indicator_def Finset.centroidWeightsIndicator_def
+-/
#print Finset.sum_centroidWeightsIndicator /-
/-- The sum of the weights for the centroid indexed by a `fintype`. -/
@@ -960,6 +1120,7 @@ theorem sum_centroidWeightsIndicator [Fintype ι] :
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
-/
+#print Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero /-
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is not
zero. -/
@@ -969,7 +1130,9 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_card_ne_zero k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero
+-/
+#print Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty /-
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the set is nonempty. -/
theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι] (h : s.Nonempty) :
@@ -978,7 +1141,9 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_nonempty k h
#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty
+-/
+#print Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one /-
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fintype ι] {n : ℕ}
@@ -987,16 +1152,18 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fin
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_card_eq_add_one k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one
+-/
-include V
-
+#print Finset.centroid_eq_affineCombination_fintype /-
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
s.centroid k p = univ.affineCombination k p (s.centroidWeightsIndicator k) :=
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+#print Finset.centroid_eq_centroid_image_of_inj_on /-
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
stated in terms of a set equal to the image to provide control of
@@ -1030,9 +1197,11 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
change p (f' x) = ↑x
rw [(hf' x).2]
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+#print Finset.centroid_eq_of_inj_on_of_image_eq /-
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
have the same centroid. -/
@@ -1043,6 +1212,7 @@ theorem centroid_eq_of_inj_on_of_image_eq {p : ι → P}
classical rw [s.centroid_eq_centroid_image_of_inj_on k hi rfl,
s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eq
+-/
end Finset
@@ -1053,8 +1223,7 @@ variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
variable {ι : Type _}
-include V
-
+#print weightedVSub_mem_vectorSpan /-
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in s, w i = 0) (p : ι → P) :
@@ -1075,7 +1244,9 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in
simp [w', Set.indicator_apply, if_pos hi]
· exact fun _ => zero_smul k _
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
+-/
+#print affineCombination_mem_affineSpan /-
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
nontrivial. -/
@@ -1100,9 +1271,11 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
#align affine_combination_mem_affine_span affineCombination_mem_affineSpan
+-/
variable (k) {V}
+#print mem_vectorSpan_iff_eq_weightedVSub /-
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
@@ -1144,9 +1317,11 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
· rintro ⟨s, w, hw, rfl⟩
exact weightedVSub_mem_vectorSpan hw p
#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSub
+-/
variable {k}
+#print eq_affineCombination_of_mem_affineSpan /-
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
@@ -1181,7 +1356,9 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
· simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
· rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
+-/
+#print eq_affineCombination_of_mem_affineSpan_of_fintype /-
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
@@ -1191,9 +1368,11 @@ theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P}
simp only [Finset.mem_coe, Set.indicator_apply, ← hw]
rw [Fintype.sum_extend_by_zero s w]
#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintype
+-/
variable (k V)
+#print mem_affineSpan_iff_eq_affineCombination /-
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
@@ -1206,7 +1385,9 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
· rintro ⟨s, w, hw, rfl⟩
exact affineCombination_mem_affineSpan hw p
#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombination
+-/
+#print mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd /-
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
weights that are not required to sum to 1. -/
@@ -1231,9 +1412,11 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
(insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
exact affineCombination_mem_affineSpan h₁ p
#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd
+-/
variable {k V}
+#print affineSpan_eq_affineSpan_lineMap_units /-
/-- Given a set of points, together with a chosen base point in this set, if we affinely transport
all other members of the set along the line joining them to this base point, the affine span is
unchanged. -/
@@ -1250,6 +1433,7 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
[use fun x => μ x * ↑(w x); use fun x => μ x * ↑(w x)⁻¹] <;>
simp [smul_smul]
#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_units
+-/
end AffineSpace'
@@ -1259,39 +1443,45 @@ variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V
variable [affine_space V P] {ι : Type _}
-include V
-
open Set Finset
+#print centroid_mem_affineSpan_of_cast_card_ne_zero /-
/-- The centroid lies in the affine span if the number of points,
converted to `k`, is not zero. -/
theorem centroid_mem_affineSpan_of_cast_card_ne_zero {s : Finset ι} (p : ι → P)
(h : (card s : k) ≠ 0) : s.centroid k p ∈ affineSpan k (range p) :=
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_cast_card_ne_zero h) p
#align centroid_mem_affine_span_of_cast_card_ne_zero centroid_mem_affineSpan_of_cast_card_ne_zero
+-/
variable (k)
+#print centroid_mem_affineSpan_of_card_ne_zero /-
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is not zero. -/
theorem centroid_mem_affineSpan_of_card_ne_zero [CharZero k] {s : Finset ι} (p : ι → P)
(h : card s ≠ 0) : s.centroid k p ∈ affineSpan k (range p) :=
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_card_ne_zero k h) p
#align centroid_mem_affine_span_of_card_ne_zero centroid_mem_affineSpan_of_card_ne_zero
+-/
+#print centroid_mem_affineSpan_of_nonempty /-
/-- In the characteristic zero case, the centroid lies in the affine
span if the set is nonempty. -/
theorem centroid_mem_affineSpan_of_nonempty [CharZero k] {s : Finset ι} (p : ι → P)
(h : s.Nonempty) : s.centroid k p ∈ affineSpan k (range p) :=
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_nonempty k h) p
#align centroid_mem_affine_span_of_nonempty centroid_mem_affineSpan_of_nonempty
+-/
+#print centroid_mem_affineSpan_of_card_eq_add_one /-
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is `n + 1`. -/
theorem centroid_mem_affineSpan_of_card_eq_add_one [CharZero k] {s : Finset ι} (p : ι → P) {n : ℕ}
(h : card s = n + 1) : s.centroid k p ∈ affineSpan k (range p) :=
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_card_eq_add_one k h) p
#align centroid_mem_affine_span_of_card_eq_add_one centroid_mem_affineSpan_of_card_eq_add_one
+-/
end DivisionRing
@@ -1301,8 +1491,7 @@ variable {k : Type _} {V : Type _} (P : Type _) [CommRing k] [AddCommGroup V] [M
variable [affine_space V P] {ι : Type _} (s : Finset ι)
-include V
-
+#print AffineMap.weightedVSubOfPoint /-
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
@@ -1314,6 +1503,7 @@ def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
simp [LinearMap.sum_apply, Finset.weightedVSubOfPoint, vsub_vadd_eq_vsub_sub, vadd_vsub_assoc,
add_sub, ← sub_add_eq_add_sub, smul_add, Finset.sum_add_distrib]
#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPoint
+-/
end AffineMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -121,7 +121,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
-theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 0)
+theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 0)
(b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w = s.weightedVSubOfPoint p b₂ w :=
by
apply eq_of_sub_eq_zero
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
-theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 1)
+theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 1)
(b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w +ᵥ b₁ = s.weightedVSubOfPoint p b₂ w +ᵥ b₂ :=
by
erw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← @vsub_eq_zero_iff_eq V,
@@ -198,8 +198,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι → P) (b : P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) =
- s.weightedVSubOfPoint p₁ b w - s.weightedVSubOfPoint p₂ b w :=
+ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.weightedVSubOfPoint p₁ b w - s.weightedVSubOfPoint p₂ b w :=
by
simp_rw [weighted_vsub_of_point_apply, ← sum_sub_distrib, ← smul_sub, vsub_sub_vsub_cancel_right]
#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub
@@ -207,15 +206,15 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι → P) (p₂ b : P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSubOfPoint p₁ b w - (∑ i in s, w i) • (p₂ -ᵥ b) :=
- by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
+ ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.weightedVSubOfPoint p₁ b w - (∑ i in s, w i) • (p₂ -ᵥ b) := by
+ rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι → P) (p₁ b : P) :
- (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = (∑ i in s, w i) • (p₁ -ᵥ b) - s.weightedVSubOfPoint p₂ b w :=
- by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
+ ∑ i in s, w i • (p₁ -ᵥ p₂ i) = (∑ i in s, w i) • (p₁ -ᵥ b) - s.weightedVSubOfPoint p₂ b w := by
+ rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
/-- A weighted sum may be split into such sums over two subsets. -/
@@ -286,14 +285,14 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
- (h : (∑ i in s, w i) = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
+ (h : ∑ i in s, w i = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
s.weightedVSubOfPoint_eq_of_sum_eq_zero w p h _ _
#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@[simp]
-theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 0) :
+theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 0) :
s.weightedVSub (fun _ => p) w = 0 := by
rw [weighted_vsub, weighted_vsub_of_point_apply_const, h, zero_smul]
#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_const
@@ -329,21 +328,21 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.weightedVSub p₁ w - s.weightedVSub p₂ w :=
+ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.weightedVSub p₁ w - s.weightedVSub p₂ w :=
s.sum_smul_vsub_eq_weightedVSubOfPoint_sub _ _ _ _
#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_sub
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSub p₁ w := by
+ (h : ∑ i in s, w i = 0) : ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.weightedVSub p₁ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, sub_zero]
#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = -s.weightedVSub p₂ w := by
+ (h : ∑ i in s, w i = 0) : ∑ i in s, w i • (p₁ -ᵥ p₂ i) = -s.weightedVSub p₂ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, zero_sub]
#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
@@ -420,7 +419,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
-theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 1) :
+theorem affineCombination_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 1) :
s.affineCombination k (fun _ => p) w = p := by
rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
@@ -435,7 +434,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
- (h : (∑ i in s, w i) = 1) (b : P) :
+ (h : ∑ i in s, w i = 1) (b : P) :
s.affineCombination k p w = s.weightedVSubOfPoint p b w +ᵥ b :=
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
@@ -486,7 +485,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
combinations. -/
@[simp]
theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (w : ι → k)
- (hw : (∑ i in s, w i) = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
+ (hw : ∑ i in s, w i = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
simp [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw 0]
#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combination
@@ -498,7 +497,7 @@ and has weight 1 and the other points in the set have weight 0. -/
theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i : ι} (his : i ∈ s)
(hwi : w i = 1) (hw0 : ∀ i2 ∈ s, i2 ≠ i → w i2 = 0) : s.affineCombination k p w = p i :=
by
- have h1 : (∑ i in s, w i) = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
+ have h1 : ∑ i in s, w i = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
rw [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p h1 (p i),
weighted_vsub_of_point_apply]
convert zero_vadd V (p i)
@@ -529,7 +528,7 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.affineCombination k p₁ w -ᵥ s.affineCombination k p₂ w :=
+ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = s.affineCombination k p₁ w -ᵥ s.affineCombination k p₂ w :=
by
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
@@ -538,15 +537,15 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.affineCombination k p₁ w -ᵥ p₂ :=
- by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
+ (h : ∑ i in s, w i = 1) : ∑ i in s, w i • (p₁ i -ᵥ p₂) = s.affineCombination k p₁ w -ᵥ p₂ := by
+ rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = p₁ -ᵥ s.affineCombination k p₂ w :=
- by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
+ (h : ∑ i in s, w i = 1) : ∑ i in s, w i • (p₁ -ᵥ p₂ i) = p₁ -ᵥ s.affineCombination k p₂ w := by
+ rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
@@ -601,9 +600,9 @@ corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V} {x : k} {s : Set ι}
{p : ι → P} {b : P} :
- (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = x),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint p b w) ↔
- ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = x),
+ ∃ (fs : Finset s) (w : s → k) (hw : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
by
classical
@@ -627,9 +626,9 @@ only if it can be expressed as `weighted_vsub` with sum of weights 0
for the corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι} {p : ι → P} :
- (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = 0),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : ∑ i in fs, w i = 0),
v = fs.weightedVSub p w) ↔
- ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = 0),
+ ∃ (fs : Finset s) (w : s → k) (hw : ∑ i in fs, w i = 0),
v = fs.weightedVSub (fun i : s => p i) w :=
eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
@@ -645,9 +644,9 @@ indexed family whose index type is the subtype corresponding to that
subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
- (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = 1),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : ∑ i in fs, w i = 1),
p0 = fs.affineCombination k p w) ↔
- ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = 1),
+ ∃ (fs : Finset s) (w : s → k) (hw : ∑ i in fs, w i = 1),
p0 = fs.affineCombination k (fun i : s => p i) w :=
by
simp_rw [affine_combination_apply, eq_vadd_iff_vsub_eq]
@@ -693,7 +692,7 @@ theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
- (∑ j in s, affineCombinationSingleWeights k i j) = 1 :=
+ ∑ j in s, affineCombinationSingleWeights k i j = 1 :=
by
rw [← affine_combination_single_weights_apply_self k i]
exact sum_eq_single_of_mem i h fun j _ hj => affine_combination_single_weights_apply_of_ne k hj
@@ -728,7 +727,7 @@ theorem weightedVSubVSubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi :
@[simp]
theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
- (∑ t in s, weightedVSubVSubWeights k i j t) = 0 :=
+ ∑ t in s, weightedVSubVSubWeights k i j t = 0 :=
by
simp_rw [weighted_vsub_vsub_weights, Pi.sub_apply, sum_sub_distrib]
simp [hi, hj]
@@ -773,7 +772,7 @@ theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
- (c : k) : (∑ t in s, affineCombinationLineMapWeights i j c t) = 1 :=
+ (c : k) : ∑ t in s, affineCombinationLineMapWeights i j c t = 1 :=
by
simp_rw [affine_combination_line_map_weights, Pi.add_apply, sum_add_distrib]
simp [hi, hj, ← mul_sum]
@@ -849,7 +848,7 @@ variable {k}
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0) :
- (∑ i in s, s.centroidWeights k i) = 1 := by simp [h]
+ ∑ i in s, s.centroidWeights k i = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero
variable (k)
@@ -857,20 +856,20 @@ variable (k)
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠ 0) :
- (∑ i in s, s.centroidWeights k i) = 1 := by simp [h]
+ ∑ i in s, s.centroidWeights k i = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zero
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
- (∑ i in s, s.centroidWeights k i) = 1 :=
+ ∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (ne_of_gt (card_pos.2 h))
#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonempty
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h : card s = n + 1) :
- (∑ i in s, s.centroidWeights k i) = 1 :=
+ ∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (h.symm ▸ Nat.succ_ne_zero n)
#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_one
@@ -956,7 +955,7 @@ theorem centroidWeightsIndicator_def :
#print Finset.sum_centroidWeightsIndicator /-
/-- The sum of the weights for the centroid indexed by a `fintype`. -/
theorem sum_centroidWeightsIndicator [Fintype ι] :
- (∑ i, s.centroidWeightsIndicator k i) = ∑ i in s, s.centroidWeights k i :=
+ ∑ i, s.centroidWeightsIndicator k i = ∑ i in s, s.centroidWeights k i :=
(Set.sum_indicator_subset _ (subset_univ _)).symm
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
-/
@@ -965,7 +964,7 @@ theorem sum_centroidWeightsIndicator [Fintype ι] :
indexed by a `fintype` sum to 1 if the number of points is not
zero. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintype ι]
- (h : card s ≠ 0) : (∑ i, s.centroidWeightsIndicator k i) = 1 :=
+ (h : card s ≠ 0) : ∑ i, s.centroidWeightsIndicator k i = 1 :=
by
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_card_ne_zero k h
@@ -974,7 +973,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the set is nonempty. -/
theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι] (h : s.Nonempty) :
- (∑ i, s.centroidWeightsIndicator k i) = 1 :=
+ ∑ i, s.centroidWeightsIndicator k i = 1 :=
by
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_nonempty k h
@@ -983,7 +982,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fintype ι] {n : ℕ}
- (h : card s = n + 1) : (∑ i, s.centroidWeightsIndicator k i) = 1 :=
+ (h : card s = n + 1) : ∑ i, s.centroidWeightsIndicator k i = 1 :=
by
rw [sum_centroid_weights_indicator]
exact s.sum_centroid_weights_eq_one_of_card_eq_add_one k h
@@ -1058,8 +1057,8 @@ include V
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
-theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
- (p : ι → P) : s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
+theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in s, w i = 0) (p : ι → P) :
+ s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
classical
rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
· skip; simp [Finset.eq_empty_of_isEmpty s]
@@ -1081,14 +1080,14 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
`affine_span` of an indexed family, if the underlying ring is
nontrivial. -/
theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι → k}
- (h : (∑ i in s, w i) = 1) (p : ι → P) :
- s.affineCombination k p w ∈ affineSpan k (Set.range p) := by
+ (h : ∑ i in s, w i = 1) (p : ι → P) : s.affineCombination k p w ∈ affineSpan k (Set.range p) :=
+ by
classical
- have hnz : (∑ i in s, w i) ≠ 0 := h.symm ▸ one_ne_zero
+ have hnz : ∑ i in s, w i ≠ 0 := h.symm ▸ one_ne_zero
have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
cases' hn with i1 hi1
let w1 : ι → k := Function.update (Function.const ι 0) i1 1
- have hw1 : (∑ i in s, w1 i) = 1 := by
+ have hw1 : ∑ i in s, w1 i = 1 := by
rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
have hw1s : s.affine_combination k p w1 = p i1 :=
s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
@@ -1108,7 +1107,7 @@ variable (k) {V}
if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (h : (∑ i in s, w i) = 0), v = s.weightedVSub p w :=
+ ∃ (s : Finset ι) (w : ι → k) (h : ∑ i in s, w i = 0), v = s.weightedVSub p w :=
by
classical
constructor
@@ -1121,7 +1120,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
(l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
hwdef
use w
- have hw : (∑ i in insert i0 l.support, w i) = 0 :=
+ have hw : ∑ i in insert i0 l.support, w i = 0 :=
by
rw [hwdef]
simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
@@ -1132,7 +1131,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
- change (∑ i in l.support, l i • _) = _
+ change ∑ i in l.support, l i • _ = _
congr with i
by_cases h : i = i0
· simp [h]
@@ -1153,7 +1152,7 @@ variable {k}
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (s : Finset ι) (w : ι → k) (hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
@@ -1165,14 +1164,14 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
rcases hd with ⟨s, w, h, hs⟩
let s' := insert i0 s
let w' := Set.indicator (↑s) w
- have h' : (∑ i in s', w' i) = 0 := by
+ have h' : ∑ i in s', w' i = 0 := by
rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
by
rw [hs]
exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
let w0 : ι → k := Function.update (Function.const ι 0) i0 1
- have hw0 : (∑ i in s', w0 i) = 1 := by
+ have hw0 : ∑ i in s', w0 i = 1 := by
rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
have hw0s : s'.affine_combination k p w0 = p i0 :=
s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
@@ -1185,7 +1184,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k) (hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
+ ∃ (w : ι → k) (hw : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
classical
obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
refine' ⟨(s : Set ι).indicator w, _, Finset.affineCombination_indicator_subset w p s.subset_univ⟩
@@ -1200,7 +1199,7 @@ if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w :=
+ ∃ (s : Finset ι) (w : ι → k) (hw : ∑ i in s, w i = 1), p1 = s.affineCombination k p w :=
by
constructor
· exact eq_affineCombination_of_mem_affineSpan
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -997,7 +997,7 @@ theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
stated in terms of a set equal to the image to provide control of
@@ -1032,8 +1032,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
rw [(hf' x).2]
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
have the same centroid. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -469,7 +469,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
- univ_eq_attach, attach_image_coe]
+ univ_eq_attach, attach_image_coe]
#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coe
omit S
@@ -564,13 +564,12 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
(hw : s.weightedVSub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
(hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by
classical
- rw [← @vsub_eq_zero_iff_eq V, ← hw, ←
- s.affine_combination_sdiff_sub (singleton_subset_iff.2 his), sdiff_singleton_eq_erase, ←
- filter_ne']
- congr
- refine' (affine_combination_of_eq_one_of_eq_zero _ _ _ (mem_singleton_self _) _ _).symm
- · simp [hwi]
- · simp
+ rw [← @vsub_eq_zero_iff_eq V, ← hw, ← s.affine_combination_sdiff_sub (singleton_subset_iff.2 his),
+ sdiff_singleton_eq_erase, ← filter_ne']
+ congr
+ refine' (affine_combination_of_eq_one_of_eq_zero _ _ _ (mem_singleton_self _) _ _).symm
+ · simp [hwi]
+ · simp
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
@@ -608,15 +607,15 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
by
classical
- simp_rw [weighted_vsub_of_point_apply]
- constructor
- · rintro ⟨fs, hfs, w, rfl, rfl⟩
- use fs.subtype s, fun i => w i, sum_subtype_of_mem _ hfs, (sum_subtype_of_mem _ hfs).symm
- · rintro ⟨fs, w, rfl, rfl⟩
- refine'
- ⟨fs.map (Function.Embedding.subtype _), map_subtype_subset _, fun i =>
- if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
- simp
+ simp_rw [weighted_vsub_of_point_apply]
+ constructor
+ · rintro ⟨fs, hfs, w, rfl, rfl⟩
+ use fs.subtype s, fun i => w i, sum_subtype_of_mem _ hfs, (sum_subtype_of_mem _ hfs).symm
+ · rintro ⟨fs, w, rfl, rfl⟩
+ refine'
+ ⟨fs.map (Function.Embedding.subtype _), map_subtype_subset _, fun i =>
+ if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
+ simp
#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
variable (k)
@@ -1043,7 +1042,7 @@ theorem centroid_eq_of_inj_on_of_image_eq {p : ι → P}
(hi₂ : ∀ (i) (_ : i ∈ s₂) (j) (_ : j ∈ s₂), p₂ i = p₂ j → i = j) (he : p '' ↑s = p₂ '' ↑s₂) :
s.centroid k p = s₂.centroid k p₂ := by
classical rw [s.centroid_eq_centroid_image_of_inj_on k hi rfl,
- s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
+ s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eq
end Finset
@@ -1062,20 +1061,20 @@ an indexed family. -/
theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
(p : ι → P) : s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
classical
- rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
- · skip; simp [Finset.eq_empty_of_isEmpty s]
- · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
- Finsupp.mem_span_image_iff_total,
- Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
- Finset.weightedVSubOfPoint_apply]
- let w' := Set.indicator (↑s) w
- have hwx : ∀ i, w' i ≠ 0 → i ∈ s := fun i => Set.mem_of_indicator_ne_zero
- use Finsupp.onFinset s w' hwx, Set.subset_univ _
- rw [Finsupp.total_apply, Finsupp.onFinset_sum hwx]
- · apply Finset.sum_congr rfl
- intro i hi
- simp [w', Set.indicator_apply, if_pos hi]
- · exact fun _ => zero_smul k _
+ rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
+ · skip; simp [Finset.eq_empty_of_isEmpty s]
+ · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
+ Finsupp.mem_span_image_iff_total,
+ Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
+ Finset.weightedVSubOfPoint_apply]
+ let w' := Set.indicator (↑s) w
+ have hwx : ∀ i, w' i ≠ 0 → i ∈ s := fun i => Set.mem_of_indicator_ne_zero
+ use Finsupp.onFinset s w' hwx, Set.subset_univ _
+ rw [Finsupp.total_apply, Finsupp.onFinset_sum hwx]
+ · apply Finset.sum_congr rfl
+ intro i hi
+ simp [w', Set.indicator_apply, if_pos hi]
+ · exact fun _ => zero_smul k _
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
/-- An `affine_combination` with sum of weights 1 is in the
@@ -1085,22 +1084,22 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
(h : (∑ i in s, w i) = 1) (p : ι → P) :
s.affineCombination k p w ∈ affineSpan k (Set.range p) := by
classical
- have hnz : (∑ i in s, w i) ≠ 0 := h.symm ▸ one_ne_zero
- have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
- cases' hn with i1 hi1
- let w1 : ι → k := Function.update (Function.const ι 0) i1 1
- have hw1 : (∑ i in s, w1 i) = 1 := by
- rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
- have hw1s : s.affine_combination k p w1 = p i1 :=
- s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
- Function.update_noteq hne _ _
- have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
- by
- rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
- apply weightedVSub_mem_vectorSpan
- simp [Pi.sub_apply, h, hw1]
- rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
- exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
+ have hnz : (∑ i in s, w i) ≠ 0 := h.symm ▸ one_ne_zero
+ have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
+ cases' hn with i1 hi1
+ let w1 : ι → k := Function.update (Function.const ι 0) i1 1
+ have hw1 : (∑ i in s, w1 i) = 1 := by
+ rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
+ have hw1s : s.affine_combination k p w1 = p i1 :=
+ s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
+ Function.update_noteq hne _ _
+ have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
+ by
+ rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
+ apply weightedVSub_mem_vectorSpan
+ simp [Pi.sub_apply, h, hw1]
+ rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
+ exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
#align affine_combination_mem_affine_span affineCombination_mem_affineSpan
variable (k) {V}
@@ -1112,40 +1111,39 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
∃ (s : Finset ι) (w : ι → k) (h : (∑ i in s, w i) = 0), v = s.weightedVSub p w :=
by
classical
- constructor
- · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩); swap
- · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
- Finsupp.mem_span_image_iff_total]
- rintro ⟨l, hl, hv⟩
- use insert i0 l.support
- set w :=
- (l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
- hwdef
- use w
- have hw : (∑ i in insert i0 l.support, w i) = 0 :=
- by
- rw [hwdef]
- simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
- Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero,
- Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero,
- sub_self]
- use hw
- have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
- change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
- rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
- Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
- change (∑ i in l.support, l i • _) = _
- congr with i
- by_cases h : i = i0
- · simp [h]
- · simp [hwdef, h]
- · skip
- rw [Set.range_eq_empty, vectorSpan_empty, Submodule.mem_bot]
- rintro rfl
- use ∅
- simp
- · rintro ⟨s, w, hw, rfl⟩
- exact weightedVSub_mem_vectorSpan hw p
+ constructor
+ · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩); swap
+ · rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
+ Finsupp.mem_span_image_iff_total]
+ rintro ⟨l, hl, hv⟩
+ use insert i0 l.support
+ set w :=
+ (l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
+ hwdef
+ use w
+ have hw : (∑ i in insert i0 l.support, w i) = 0 :=
+ by
+ rw [hwdef]
+ simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
+ Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero,
+ Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero, sub_self]
+ use hw
+ have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
+ change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
+ rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
+ Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
+ change (∑ i in l.support, l i • _) = _
+ congr with i
+ by_cases h : i = i0
+ · simp [h]
+ · simp [hwdef, h]
+ · skip
+ rw [Set.range_eq_empty, vectorSpan_empty, Submodule.mem_bot]
+ rintro rfl
+ use ∅
+ simp
+ · rintro ⟨s, w, hw, rfl⟩
+ exact weightedVSub_mem_vectorSpan hw p
#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSub
variable {k}
@@ -1157,43 +1155,42 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (s : Finset ι) (w : ι → k) (hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
classical
- have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
- rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
- cases' hn with i0
- have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
- have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
- AffineSubspace.vsub_mem_direction h h0
- rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
- rcases hd with ⟨s, w, h, hs⟩
- let s' := insert i0 s
- let w' := Set.indicator (↑s) w
- have h' : (∑ i in s', w' i) = 0 := by
- rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
- have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
- by
- rw [hs]
- exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
- let w0 : ι → k := Function.update (Function.const ι 0) i0 1
- have hw0 : (∑ i in s', w0 i) = 1 := by
- rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
- have hw0s : s'.affine_combination k p w0 = p i0 :=
- s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
- (Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
- use s', w0 + w'
- constructor
- · simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
- · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
+ have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
+ rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
+ cases' hn with i0
+ have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
+ have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
+ AffineSubspace.vsub_mem_direction h h0
+ rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
+ rcases hd with ⟨s, w, h, hs⟩
+ let s' := insert i0 s
+ let w' := Set.indicator (↑s) w
+ have h' : (∑ i in s', w' i) = 0 := by
+ rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
+ have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
+ by
+ rw [hs]
+ exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
+ let w0 : ι → k := Function.update (Function.const ι 0) i0 1
+ have hw0 : (∑ i in s', w0 i) = 1 := by
+ rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
+ have hw0s : s'.affine_combination k p w0 = p i0 :=
+ s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
+ (Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
+ use s', w0 + w'
+ constructor
+ · simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
+ · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (w : ι → k) (hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
classical
- obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
- refine'
- ⟨(s : Set ι).indicator w, _, Finset.affineCombination_indicator_subset w p s.subset_univ⟩
- simp only [Finset.mem_coe, Set.indicator_apply, ← hw]
- rw [Fintype.sum_extend_by_zero s w]
+ obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
+ refine' ⟨(s : Set ι).indicator w, _, Finset.affineCombination_indicator_subset w p s.subset_univ⟩
+ simp only [Finset.mem_coe, Set.indicator_apply, ← hw]
+ rw [Fintype.sum_extend_by_zero s w]
#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintype
variable (k V)
@@ -1224,16 +1221,16 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
exact ⟨s, w, s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw (p j)⟩
· rintro ⟨s, w, rfl⟩
classical
- let w' : ι → k := Function.update w j (1 - (s \ {j}).Sum w)
- have h₁ : (insert j s).Sum w' = 1 := by
- by_cases hj : j ∈ s
- · simp [Finset.sum_update_of_mem hj, Finset.insert_eq_of_mem hj]
- · simp [w', Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
- have hww : ∀ i, i ≠ j → w i = w' i := by intro i hij; simp [w', hij]
- rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
- s.weighted_vsub_of_point_insert w' p j, ←
- (insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
- exact affineCombination_mem_affineSpan h₁ p
+ let w' : ι → k := Function.update w j (1 - (s \ {j}).Sum w)
+ have h₁ : (insert j s).Sum w' = 1 := by
+ by_cases hj : j ∈ s
+ · simp [Finset.sum_update_of_mem hj, Finset.insert_eq_of_mem hj]
+ · simp [w', Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
+ have hww : ∀ i, i ≠ j → w i = w' i := by intro i hij; simp [w', hij]
+ rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
+ s.weighted_vsub_of_point_insert w' p j, ←
+ (insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
+ exact affineCombination_mem_affineSpan h₁ p
#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd
variable {k V}
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -602,9 +602,9 @@ corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V} {x : k} {s : Set ι}
{p : ι → P} {b : P} :
- (∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = x),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = x),
v = fs.weightedVSubOfPoint p b w) ↔
- ∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = x),
+ ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = x),
v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
by
classical
@@ -628,9 +628,9 @@ only if it can be expressed as `weighted_vsub` with sum of weights 0
for the corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι} {p : ι → P} :
- (∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = 0),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = 0),
v = fs.weightedVSub p w) ↔
- ∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = 0),
+ ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = 0),
v = fs.weightedVSub (fun i : s => p i) w :=
eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
@@ -646,9 +646,9 @@ indexed family whose index type is the subtype corresponding to that
subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
- (∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = 1),
+ (∃ (fs : Finset ι) (hfs : ↑fs ⊆ s) (w : ι → k) (hw : (∑ i in fs, w i) = 1),
p0 = fs.affineCombination k p w) ↔
- ∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = 1),
+ ∃ (fs : Finset s) (w : s → k) (hw : (∑ i in fs, w i) = 1),
p0 = fs.affineCombination k (fun i : s => p i) w :=
by
simp_rw [affine_combination_apply, eq_vadd_iff_vsub_eq]
@@ -892,7 +892,7 @@ theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (
#align finset.centroid_def Finset.centroid_def
theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id := by
- rw [centroid, centroid, ← s.attach_affine_combination_coe]; congr ; ext; simp
+ rw [centroid, centroid, ← s.attach_affine_combination_coe]; congr; ext; simp
#align finset.centroid_univ Finset.centroid_univ
/-- The centroid of a single point. -/
@@ -1109,7 +1109,7 @@ variable (k) {V}
if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k)(h : (∑ i in s, w i) = 0), v = s.weightedVSub p w :=
+ ∃ (s : Finset ι) (w : ι → k) (h : (∑ i in s, w i) = 0), v = s.weightedVSub p w :=
by
classical
constructor
@@ -1131,7 +1131,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
sub_self]
use hw
have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
- change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
+ change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
change (∑ i in l.support, l i • _) = _
@@ -1155,15 +1155,15 @@ variable {k}
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k) (hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
- rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
+ rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
cases' hn with i0
have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
AffineSubspace.vsub_mem_direction h h0
- rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
+ rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
rcases hd with ⟨s, w, h, hs⟩
let s' := insert i0 s
let w' := Set.indicator (↑s) w
@@ -1187,7 +1187,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k)(hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
+ ∃ (w : ι → k) (hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
classical
obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
refine'
@@ -1203,7 +1203,7 @@ if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w :=
+ ∃ (s : Finset ι) (w : ι → k) (hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w :=
by
constructor
· exact eq_affineCombination_of_mem_affineSpan
@@ -1216,7 +1216,7 @@ affine span of this family corresponds to an identity in terms of `weighted_vsub
weights that are not required to sum to 1. -/
theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι → P) (j : ι) (q : P) :
q ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k), q = s.weightedVSubOfPoint p (p j) w +ᵥ p j :=
+ ∃ (s : Finset ι) (w : ι → k), q = s.weightedVSubOfPoint p (p j) w +ᵥ p j :=
by
constructor
· intro hq
@@ -1248,10 +1248,10 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
have : s = Set.range (coe : s → P) := by simp
conv_rhs => rw [this]
apply le_antisymm <;> intro q hq <;>
- erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq⊢ <;>
+ erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq ⊢ <;>
obtain ⟨t, μ, rfl⟩ := hq <;>
use t <;>
- [use fun x => μ x * ↑(w x);use fun x => μ x * ↑(w x)⁻¹] <;>
+ [use fun x => μ x * ↑(w x); use fun x => μ x * ↑(w x)⁻¹] <;>
simp [smul_smul]
#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_units
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -52,7 +52,7 @@ These definitions are for sums over a `finset`; versions for a
noncomputable section
-open BigOperators Affine
+open scoped BigOperators Affine
namespace Finset
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -56,12 +56,6 @@ open BigOperators Affine
namespace Finset
-/- warning: finset.univ_fin2 -> Finset.univ_fin2 is a dubious translation:
-lean 3 declaration is
- Eq.{1} (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Insert.insert.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.hasInsert.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (b : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) a b)) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (Singleton.singleton.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.hasSingleton.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
-but is expected to have type
- Eq.{1} (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Insert.insert.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instInsertFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a b)) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Singleton.singleton.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instSingletonFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
-Case conversion may be inaccurate. Consider using '#align finset.univ_fin2 Finset.univ_fin2ₓ'. -/
theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} := by ext x; fin_cases x <;> simp
#align finset.univ_fin2 Finset.univ_fin2
@@ -87,18 +81,12 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
#align finset.weighted_vsub_of_point Finset.weightedVSubOfPoint
-/
-/- warning: finset.weighted_vsub_of_point_apply -> Finset.weightedVSubOfPoint_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
s.weightedVSubOfPoint p b w = ∑ i in s, w i • (p i -ᵥ b) := by
simp [weighted_vsub_of_point, LinearMap.sum_apply]
#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_apply
-/- warning: finset.weighted_vsub_of_point_apply_const -> Finset.weightedVSubOfPoint_apply_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
@@ -106,9 +94,6 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
rw [weighted_vsub_of_point_apply, sum_smul]
#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_const
-/- warning: finset.weighted_vsub_of_point_congr -> Finset.weightedVSubOfPoint_congr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
@@ -120,9 +105,6 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
rw [hw i hi, hp i hi]
#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congr
-/- warning: finset.weighted_vsub_of_point_eq_of_weights_eq -> Finset.weightedVSubOfPoint_eq_of_weights_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂ : ι → k)
@@ -137,9 +119,6 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
· simp [hw i h]
#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eq
-/- warning: finset.weighted_vsub_of_point_eq_of_sum_eq_zero -> Finset.weightedVSubOfPoint_eq_of_sum_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 0)
@@ -155,9 +134,6 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
rw [← sum_smul, h, zero_smul]
#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zero
-/- warning: finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one -> Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 1)
@@ -176,9 +152,6 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
rw [← sum_smul, h, one_smul, vsub_add_vsub_cancel, vsub_self]
#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one
-/- warning: finset.weighted_vsub_of_point_erase -> Finset.weightedVSubOfPoint_erase is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@[simp]
@@ -190,9 +163,6 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
rw [vsub_self, smul_zero]
#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_erase
-/- warning: finset.weighted_vsub_of_point_insert -> Finset.weightedVSubOfPoint_insert is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@[simp]
@@ -204,9 +174,6 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
rw [vsub_self, smul_zero]
#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insert
-/- warning: finset.weighted_vsub_of_point_indicator_subset -> Finset.weightedVSubOfPoint_indicator_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b : P) {s₁ s₂ : Finset ι}
@@ -218,9 +185,6 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
Set.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
-/- warning: finset.weighted_vsub_of_point_map -> Finset.weightedVSubOfPoint_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
`finset`. -/
@@ -231,9 +195,6 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
exact Finset.sum_map _ _ _
#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_map
-/- warning: finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι → P) (b : P) :
@@ -243,9 +204,6 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
simp_rw [weighted_vsub_of_point_apply, ← sum_sub_distrib, ← smul_sub, vsub_sub_vsub_cancel_right]
#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub
-/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι → P) (p₂ b : P) :
@@ -253,9 +211,6 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub
-/- warning: finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point -> Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι → P) (p₁ b : P) :
@@ -263,9 +218,6 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
-/- warning: finset.weighted_vsub_of_point_sdiff -> Finset.weightedVSubOfPoint_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
@@ -274,9 +226,6 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
by simp_rw [weighted_vsub_of_point_apply, sum_sdiff h]
#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiff
-/- warning: finset.weighted_vsub_of_point_sdiff_sub -> Finset.weightedVSubOfPoint_sdiff_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
@@ -285,9 +234,6 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
by rw [map_neg, sub_neg_eq_add, s.weighted_vsub_of_point_sdiff h]
#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_sub
-/- warning: finset.weighted_vsub_of_point_subtype_eq_filter -> Finset.weightedVSubOfPoint_subtype_eq_filter is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -296,9 +242,6 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
by rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← sum_subtype_eq_sum_filter]
#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filter
-/- warning: finset.weighted_vsub_of_point_filter_of_ne -> Finset.weightedVSubOfPoint_filter_of_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {pred : ι → Prop}
@@ -312,9 +255,6 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
simpa [hw] using hne
#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_ne
-/- warning: finset.weighted_vsub_of_point_const_smul -> Finset.weightedVSubOfPoint_const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
theorem weightedVSubOfPoint_const_smul (w : ι → k) (p : ι → P) (b : P) (c : k) :
@@ -332,12 +272,6 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
#align finset.weighted_vsub Finset.weightedVSub
-/
-/- warning: finset.weighted_vsub_apply -> Finset.weightedVSub_apply is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
that base point will cancel out later); a more typical use case for
@@ -349,9 +283,6 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
simp [weighted_vsub, LinearMap.sum_apply]
#align finset.weighted_vsub_apply Finset.weightedVSub_apply
-/- warning: finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero -> Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
@@ -359,9 +290,6 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
s.weightedVSubOfPoint_eq_of_sum_eq_zero w p h _ _
#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
-/- warning: finset.weighted_vsub_apply_const -> Finset.weightedVSub_apply_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@[simp]
@@ -370,21 +298,12 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
rw [weighted_vsub, weighted_vsub_of_point_apply_const, h, zero_smul]
#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_const
-/- warning: finset.weighted_vsub_empty -> Finset.weightedVSub_empty is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).weightedVSub p w = (0 : V) := by
simp [weighted_vsub_apply]
#align finset.weighted_vsub_empty Finset.weightedVSub_empty
-/- warning: finset.weighted_vsub_congr -> Finset.weightedVSub_congr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
@@ -392,9 +311,6 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
s.weightedVSubOfPoint_congr hw hp _
#align finset.weighted_vsub_congr Finset.weightedVSub_congr
-/- warning: finset.weighted_vsub_indicator_subset -> Finset.weightedVSub_indicator_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι} (h : s₁ ⊆ s₂) :
@@ -402,9 +318,6 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
weightedVSubOfPoint_indicator_subset _ _ _ h
#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subset
-/- warning: finset.weighted_vsub_map -> Finset.weightedVSub_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
original `finset`. -/
@@ -413,9 +326,6 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
s₂.weightedVSubOfPoint_map _ _ _ _
#align finset.weighted_vsub_map Finset.weightedVSub_map
-/- warning: finset.sum_smul_vsub_eq_weighted_vsub_sub -> Finset.sum_smul_vsub_eq_weightedVSub_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P) :
@@ -423,9 +333,6 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
s.sum_smul_vsub_eq_weightedVSubOfPoint_sub _ _ _ _
#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_sub
-/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub -> Finset.sum_smul_vsub_const_eq_weightedVSub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p₂ : P)
@@ -433,9 +340,6 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, sub_zero]
#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
-/- warning: finset.sum_smul_const_vsub_eq_neg_weighted_vsub -> Finset.sum_smul_const_vsub_eq_neg_weightedVSub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P) (p₁ : P)
@@ -443,27 +347,18 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, zero_sub]
#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
-/- warning: finset.weighted_vsub_sdiff -> Finset.weightedVSub_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
(s \ s₂).weightedVSub p w + s₂.weightedVSub p w = s.weightedVSub p w :=
s.weightedVSubOfPoint_sdiff h _ _ _
#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiff
-/- warning: finset.weighted_vsub_sdiff_sub -> Finset.weightedVSub_sdiff_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) : (s \ s₂).weightedVSub p w - s₂.weightedVSub p (-w) = s.weightedVSub p w :=
s.weightedVSubOfPoint_sdiff_sub h _ _ _
#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_sub
-/- warning: finset.weighted_vsub_subtype_eq_filter -> Finset.weightedVSub_subtype_eq_filter is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -472,9 +367,6 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
s.weightedVSubOfPoint_subtype_eq_filter _ _ _ _
#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filter
-/- warning: finset.weighted_vsub_filter_of_ne -> Finset.weightedVSub_filter_of_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop} [DecidablePred pred]
@@ -482,9 +374,6 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
s.weightedVSubOfPoint_filter_of_ne _ _ _ h
#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_ne
-/- warning: finset.weighted_vsub_const_smul -> Finset.weightedVSub_const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
s.weightedVSub p (c • w) = c • s.weightedVSub p w :=
@@ -493,12 +382,6 @@ theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
variable (k)
-/- warning: finset.affine_combination -> Finset.affineCombination is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S)
-but is expected to have type
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u1 u4, max u1 u4, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S)
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination Finset.affineCombinationₓ'. -/
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
the weights. This is intended to be used when the sum of the weights
@@ -512,12 +395,6 @@ def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
map_vadd' w₁ w₂ := by simp_rw [vadd_vadd, weighted_vsub, vadd_eq_add, LinearMap.map_add]
#align finset.affine_combination Finset.affineCombination
-/- warning: finset.affine_combination_linear -> Finset.affineCombination_linear is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u1} (ι -> k) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (AffineMap.linear.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)
-but is expected to have type
- forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> P), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u4 u2, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u2} (ι -> k) (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (AffineMap.linear.{u4, max u4 u2, max u4 u2, u3, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u2} k _inst_1 ι) _inst_2 _inst_3 S (Finset.affineCombination.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_linear Finset.affineCombination_linearₓ'. -/
/-- The linear map corresponding to `affine_combination` is
`weighted_vsub`. -/
@[simp]
@@ -528,9 +405,6 @@ theorem affineCombination_linear (p : ι → P) :
variable {k}
-/- warning: finset.affine_combination_apply -> Finset.affineCombination_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
when that base point will cancel out later); a more typical use case
@@ -544,9 +418,6 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
rfl
#align finset.affine_combination_apply Finset.affineCombination_apply
-/- warning: finset.affine_combination_apply_const -> Finset.affineCombination_apply_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 1) :
@@ -554,9 +425,6 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
-/- warning: finset.affine_combination_congr -> Finset.affineCombination_congr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
@@ -564,9 +432,6 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
simp_rw [affine_combination_apply, s.weighted_vsub_of_point_congr hw hp]
#align finset.affine_combination_congr Finset.affineCombination_congr
-/- warning: finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one -> Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
@@ -575,27 +440,18 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
-/- warning: finset.weighted_vsub_vadd_affine_combination -> Finset.weightedVSub_vadd_affineCombination is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
s.weightedVSub p w₁ +ᵥ s.affineCombination k p w₂ = s.affineCombination k p (w₁ + w₂) := by
rw [← vadd_eq_add, AffineMap.map_vadd, affine_combination_linear]
#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombination
-/- warning: finset.affine_combination_vsub -> Finset.affineCombination_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
s.affineCombination k p w₁ -ᵥ s.affineCombination k p w₂ = s.weightedVSub p (w₁ - w₂) := by
rw [← AffineMap.linearMap_vsub, affine_combination_linear, vsub_eq_sub]
#align finset.affine_combination_vsub Finset.affineCombination_vsub
-/- warning: finset.attach_affine_combination_of_injective -> Finset.attach_affineCombination_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w :=
@@ -610,9 +466,6 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
exact fun _ _ _ _ hxy => hf hxy
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
-/- warning: finset.attach_affine_combination_coe -> Finset.attach_affineCombination_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
@@ -621,12 +474,6 @@ theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
omit S
-/- warning: finset.weighted_vsub_eq_linear_combination -> Finset.weightedVSub_eq_linear_combination is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@[simp]
@@ -635,9 +482,6 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
simp [s.weighted_vsub_apply, vsub_eq_sub, smul_sub, ← Finset.sum_smul, hw]
#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combination
-/- warning: finset.affine_combination_eq_linear_combination -> Finset.affineCombination_eq_linear_combination is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@[simp]
@@ -648,9 +492,6 @@ theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (
include S
-/- warning: finset.affine_combination_of_eq_one_of_eq_zero -> Finset.affineCombination_of_eq_one_of_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@[simp]
@@ -668,9 +509,6 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
· simp [hw0 i2 hi2 h]
#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zero
-/- warning: finset.affine_combination_indicator_subset -> Finset.affineCombination_indicator_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι}
@@ -680,9 +518,6 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
weighted_vsub_of_point_indicator_subset _ _ _ h]
#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subset
-/- warning: finset.affine_combination_map -> Finset.affineCombination_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
`finset`. -/
@@ -691,9 +526,6 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
simp_rw [affine_combination_apply, weighted_vsub_of_point_map]
#align finset.affine_combination_map Finset.affineCombination_map
-/- warning: finset.sum_smul_vsub_eq_affine_combination_vsub -> Finset.sum_smul_vsub_eq_affineCombination_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
@@ -703,9 +535,6 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsub
-/- warning: finset.sum_smul_vsub_const_eq_affine_combination_vsub -> Finset.sum_smul_vsub_const_eq_affineCombination_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
@@ -713,9 +542,6 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
-/- warning: finset.sum_smul_const_vsub_eq_vsub_affine_combination -> Finset.sum_smul_const_vsub_eq_vsub_affineCombination is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
@@ -723,9 +549,6 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
-/- warning: finset.affine_combination_sdiff_sub -> Finset.affineCombination_sdiff_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) :
@@ -735,9 +558,6 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
exact s.weighted_vsub_sdiff_sub h _ _
#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_sub
-/- warning: finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one -> Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
@@ -753,9 +573,6 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
· simp
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
-/- warning: finset.affine_combination_subtype_eq_filter -> Finset.affineCombination_subtype_eq_filter is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -765,9 +582,6 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
rw [affine_combination_apply, affine_combination_apply, weighted_vsub_of_point_subtype_eq_filter]
#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filter
-/- warning: finset.affine_combination_filter_of_ne -> Finset.affineCombination_filter_of_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop}
@@ -779,9 +593,6 @@ theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι
variable {V}
-/- warning: finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype -> Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
`weighted_vsub_of_point` using a `finset` lying within that subset and
@@ -810,9 +621,6 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
variable (k)
-/- warning: finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype -> Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
a `finset` lying within that subset and with sum of weights 0 if and
@@ -829,9 +637,6 @@ theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι}
variable (V)
-/- warning: finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype -> Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
`affine_combination` using a `finset` lying within that subset and
@@ -852,9 +657,6 @@ theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s
variable {k V}
-/- warning: finset.map_affine_combination -> Finset.map_affineCombination is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.Sum w = 1) (f : P →ᵃ[k] P₂) :
@@ -880,34 +682,16 @@ def affineCombinationSingleWeights [DecidableEq ι] (i : ι) : ι → k :=
#align finset.affine_combination_single_weights Finset.affineCombinationSingleWeights
-/
-/- warning: finset.affine_combination_single_weights_apply_self -> Finset.affineCombinationSingleWeights_apply_self is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1))))
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_selfₓ'. -/
@[simp]
theorem affineCombinationSingleWeights_apply_self [DecidableEq ι] (i : ι) :
affineCombinationSingleWeights k i i = 1 := by simp [affine_combination_single_weights]
#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_self
-/- warning: finset.affine_combination_single_weights_apply_of_ne -> Finset.affineCombinationSingleWeights_apply_of_ne is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι j i) -> (Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι j i) -> (Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_single_weights_apply_of_ne Finset.affineCombinationSingleWeights_apply_of_neₓ'. -/
@[simp]
theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (h : j ≠ i) :
affineCombinationSingleWeights k i j = 0 := by simp [affine_combination_single_weights, h]
#align finset.affine_combination_single_weights_apply_of_ne Finset.affineCombinationSingleWeights_apply_of_ne
-/- warning: finset.sum_affine_combination_single_weights -> Finset.sum_affineCombinationSingleWeights is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
(∑ j in s, affineCombinationSingleWeights k i j) = 1 :=
@@ -923,56 +707,26 @@ def weightedVSubVSubWeights [DecidableEq ι] (i j : ι) : ι → k :=
#align finset.weighted_vsub_vsub_weights Finset.weightedVSubVSubWeights
-/
-/- warning: finset.weighted_vsub_vsub_weights_self -> Finset.weightedVSubVSubWeights_self is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u2 u1} (ι -> k) 0 (OfNat.mk.{max u2 u1} (ι -> k) 0 (Zero.zero.{max u2 u1} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7165 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_selfₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSubWeights k i i = 0 :=
by simp [weighted_vsub_vsub_weights]
#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_self
-/- warning: finset.weighted_vsub_vsub_weights_apply_left -> Finset.weightedVSubVSubWeights_apply_left is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_leftₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) :
weightedVSubVSubWeights k i j i = 1 := by simp [weighted_vsub_vsub_weights, h]
#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_left
-/- warning: finset.weighted_vsub_vsub_weights_apply_right -> Finset.weightedVSubVSubWeights_apply_right is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (Ring.toNeg.{u1} k _inst_1) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_rightₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) :
weightedVSubVSubWeights k i j j = -1 := by simp [weighted_vsub_vsub_weights, h.symm]
#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_right
-/- warning: finset.weighted_vsub_vsub_weights_apply_of_ne -> Finset.weightedVSubVSubWeights_apply_of_ne is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVSubVSubWeights_apply_of_neₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i) (hj : t ≠ j) :
weightedVSubVSubWeights k i j t = 0 := by simp [weighted_vsub_vsub_weights, hi, hj]
#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVSubVSubWeights_apply_of_ne
-/- warning: finset.sum_weighted_vsub_vsub_weights -> Finset.sum_weightedVSubVSubWeights is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t)) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVSubVSubWeightsₓ'. -/
@[simp]
theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
(∑ t in s, weightedVSubVSubWeights k i j t) = 0 :=
@@ -998,12 +752,6 @@ theorem affineCombinationLineMapWeights_self [DecidableEq ι] (i : ι) (c : k) :
#align finset.affine_combination_line_map_weights_self Finset.affineCombinationLineMapWeights_self
-/
-/- warning: finset.affine_combination_line_map_weights_apply_left -> Finset.affineCombinationLineMapWeights_apply_left is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) c))
-but is expected to have type
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (Ring.toSub.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) c))
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_line_map_weights_apply_left Finset.affineCombinationLineMapWeights_apply_leftₓ'. -/
@[simp]
theorem affineCombinationLineMapWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) (c : k) :
affineCombinationLineMapWeights i j c i = 1 - c := by
@@ -1018,24 +766,12 @@ theorem affineCombinationLineMapWeights_apply_right [DecidableEq ι] {i j : ι}
#align finset.affine_combination_line_map_weights_apply_right Finset.affineCombinationLineMapWeights_apply_right
-/
-/- warning: finset.affine_combination_line_map_weights_apply_of_ne -> Finset.affineCombinationLineMapWeights_apply_of_ne is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_line_map_weights_apply_of_ne Finset.affineCombinationLineMapWeights_apply_of_neₓ'. -/
@[simp]
theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i)
(hj : t ≠ j) (c : k) : affineCombinationLineMapWeights i j c t = 0 := by
simp [affine_combination_line_map_weights, hi, hj]
#align finset.affine_combination_line_map_weights_apply_of_ne Finset.affineCombinationLineMapWeights_apply_of_ne
-/- warning: finset.sum_affine_combination_line_map_weights -> Finset.sum_affineCombinationLineMapWeights is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
-but is expected to have type
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_line_map_weights Finset.sum_affineCombinationLineMapWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
(c : k) : (∑ t in s, affineCombinationLineMapWeights i j c t) = 1 :=
@@ -1048,9 +784,6 @@ include S
variable (k)
-/- warning: finset.affine_combination_affine_combination_single_weights -> Finset.affineCombination_affineCombinationSingleWeights is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p : ι → P) {i : ι}
@@ -1061,9 +794,6 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
simp [hj]
#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeights
-/- warning: finset.weighted_vsub_weighted_vsub_vsub_weights -> Finset.weightedVSub_weightedVSubVSubWeights is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@[simp]
@@ -1076,9 +806,6 @@ theorem weightedVSub_weightedVSubVSubWeights [DecidableEq ι] (p : ι → P) {i
variable {k}
-/- warning: finset.affine_combination_affine_combination_line_map_weights -> Finset.affineCombination_affineCombinationLineMapWeights is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@[simp]
@@ -1107,24 +834,12 @@ def centroidWeights : ι → k :=
#align finset.centroid_weights Finset.centroidWeights
-/
-/- warning: finset.centroid_weights_apply -> Finset.centroidWeights_apply is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) (i : ι), Eq.{succ u1} k (Finset.centroidWeights.{u1, u2} k _inst_1 ι s i) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) (i : ι), Eq.{succ u2} k (Finset.centroidWeights.{u2, u1} k _inst_1 ι s i) (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s)))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_apply Finset.centroidWeights_applyₓ'. -/
/-- `centroid_weights` at any point. -/
@[simp]
theorem centroidWeights_apply (i : ι) : s.centroidWeights k i = (card s : k)⁻¹ :=
rfl
#align finset.centroid_weights_apply Finset.centroidWeights_apply
-/- warning: finset.centroid_weights_eq_const -> Finset.centroidWeights_eq_const is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u1, u2} k _inst_1 ι s) (Function.const.{succ u1, succ u2} k ι (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s) (Function.const.{succ u2, succ u1} k ι (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s))))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_eq_const Finset.centroidWeights_eq_constₓ'. -/
/-- `centroid_weights` equals a constant function. -/
theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card s : k)⁻¹ :=
rfl
@@ -1132,12 +847,6 @@ theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card
variable {k}
-/- warning: finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero -> Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall {k : Type.{u2}} [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), (Ne.{succ u2} k (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zeroₓ'. -/
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0) :
@@ -1146,24 +855,12 @@ theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0)
variable (k)
-/- warning: finset.sum_centroid_weights_eq_one_of_card_ne_zero -> Finset.sum_centroidWeights_eq_one_of_card_ne_zero is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠ 0) :
(∑ i in s, s.centroidWeights k i) = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zero
-/- warning: finset.sum_centroid_weights_eq_one_of_nonempty -> Finset.sum_centroidWeights_eq_one_of_nonempty is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
@@ -1171,12 +868,6 @@ theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
s.sum_centroidWeights_eq_one_of_card_ne_zero k (ne_of_gt (card_pos.2 h))
#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonempty
-/- warning: finset.sum_centroid_weights_eq_one_of_card_eq_add_one -> Finset.sum_centroidWeights_eq_one_of_card_eq_add_one is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h : card s = n + 1) :
@@ -1195,42 +886,21 @@ def centroid (p : ι → P) : P :=
#align finset.centroid Finset.centroid
-/
-/- warning: finset.centroid_def -> Finset.centroid_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
rfl
#align finset.centroid_def Finset.centroid_def
-/- warning: finset.centroid_univ -> Finset.centroid_univ is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 P s (id.{succ u3} P))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s)) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 P s (id.{succ u3} P))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_univ Finset.centroid_univₓ'. -/
theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id := by
rw [centroid, centroid, ← s.attach_affine_combination_coe]; congr ; ext; simp
#align finset.centroid_univ Finset.centroid_univ
-/- warning: finset.centroid_singleton -> Finset.centroid_singleton is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P) (i : ι), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.hasSingleton.{u4} ι) i) p) (p i)
-but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (p : ι -> P) (i : ι), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) p) (p i)
-Case conversion may be inaccurate. Consider using '#align finset.centroid_singleton Finset.centroid_singletonₓ'. -/
/-- The centroid of a single point. -/
@[simp]
theorem centroid_singleton (p : ι → P) (i : ι) : ({i} : Finset ι).centroid k p = p i := by
simp [centroid_def, affine_combination_apply]
#align finset.centroid_singleton Finset.centroid_singleton
-/- warning: finset.centroid_pair -> Finset.centroid_pair is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.hasSingleton.{u4} ι) i₂)) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
-but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.instSingletonFinset.{u4} ι) i₂)) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_pair Finset.centroid_pairₓ'. -/
/-- The centroid of two points, expressed directly as adding a vector
to a point. -/
theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁ i₂ : ι) :
@@ -1249,12 +919,6 @@ theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁
simp [h]
#align finset.centroid_pair Finset.centroid_pair
-/- warning: finset.centroid_pair_fin -> Finset.centroid_pair_fin is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
-but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> P), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_pair_fin Finset.centroid_pair_finₓ'. -/
/-- The centroid of two points indexed by `fin 2`, expressed directly
as adding a vector to the first point. -/
theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
@@ -1264,12 +928,6 @@ theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
convert centroid_pair k p 0 1
#align finset.centroid_pair_fin Finset.centroid_pair_fin
-/- warning: finset.centroid_map -> Finset.centroid_map is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) (Finset.centroid.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) (Finset.centroid.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_map Finset.centroid_mapₓ'. -/
/-- A centroid, over the image of an embedding, equals a centroid with
the same points and weights over the original `finset`. -/
theorem centroid_map (e : ι₂ ↪ ι) (p : ι → P) : (s₂.map e).centroid k p = s₂.centroid k (p ∘ e) :=
@@ -1290,12 +948,6 @@ def centroidWeightsIndicator : ι → k :=
#align finset.centroid_weights_indicator Finset.centroidWeightsIndicator
-/
-/- warning: finset.centroid_weights_indicator_def -> Finset.centroidWeightsIndicator_def is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s) (Set.indicator.{u2, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s) (Finset.centroidWeights.{u1, u2} k _inst_1 ι s))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s) (Set.indicator.{u1, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)))) (Finset.toSet.{u1} ι s) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_indicator_def Finset.centroidWeightsIndicator_defₓ'. -/
/-- The definition of `centroid_weights_indicator`. -/
theorem centroidWeightsIndicator_def :
s.centroidWeightsIndicator k = Set.indicator (↑s) (s.centroidWeights k) :=
@@ -1310,12 +962,6 @@ theorem sum_centroidWeightsIndicator [Fintype ι] :
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
-/
-/- warning: finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero -> Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is not
zero. -/
@@ -1326,12 +972,6 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
exact s.sum_centroid_weights_eq_one_of_card_ne_zero k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero
-/- warning: finset.sum_centroid_weights_indicator_eq_one_of_nonempty -> Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the set is nonempty. -/
theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι] (h : s.Nonempty) :
@@ -1341,12 +981,6 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
exact s.sum_centroid_weights_eq_one_of_nonempty k h
#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty
-/- warning: finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one -> Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
-but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fintype ι] {n : ℕ}
@@ -1358,21 +992,12 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fin
include V
-/- warning: finset.centroid_eq_affine_combination_fintype -> Finset.centroid_eq_affineCombination_fintype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
s.centroid k p = univ.affineCombination k p (s.centroidWeightsIndicator k) :=
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/- warning: finset.centroid_eq_centroid_image_of_inj_on -> Finset.centroid_eq_centroid_image_of_inj_on is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {p : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (forall (j : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {ps : Set.{u3} P} [_inst_5 : Fintype.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps)], (Eq.{succ u3} (Set.{u3} P) ps (Set.image.{u4, u3} ι P p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s))) -> (Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) _inst_5) (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x ps))))) x))))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {p : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall (j : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {ps : Set.{u3} P} [_inst_5 : Fintype.{u3} (Set.Elem.{u3} P ps)], (Eq.{succ u3} (Set.{u3} P) ps (Set.image.{u4, u3} ι P p (Finset.toSet.{u4} ι s))) -> (Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.Elem.{u3} P ps) (Finset.univ.{u3} (Set.Elem.{u3} P ps) _inst_5) (fun (x : Set.Elem.{u3} P ps) => Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) x ps) x))))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_onₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
@@ -1408,12 +1033,6 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
rw [(hf' x).2]
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/- warning: finset.centroid_eq_of_inj_on_of_image_eq -> Finset.centroid_eq_of_inj_on_of_image_eq is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) {p : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (forall (j : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {p₂ : ι₂ -> P}, (forall (i : ι₂), (Membership.Mem.{u5, u5} ι₂ (Finset.{u5} ι₂) (Finset.hasMem.{u5} ι₂) i s₂) -> (forall (j : ι₂), (Membership.Mem.{u5, u5} ι₂ (Finset.{u5} ι₂) (Finset.hasMem.{u5} ι₂) j s₂) -> (Eq.{succ u3} P (p₂ i) (p₂ j)) -> (Eq.{succ u5} ι₂ i j))) -> (Eq.{succ u3} (Set.{u3} P) (Set.image.{u4, u3} ι P p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s)) (Set.image.{u5, u3} ι₂ P p₂ ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (Finset.{u5} ι₂) (Set.{u5} ι₂) (HasLiftT.mk.{succ u5, succ u5} (Finset.{u5} ι₂) (Set.{u5} ι₂) (CoeTCₓ.coe.{succ u5, succ u5} (Finset.{u5} ι₂) (Set.{u5} ι₂) (Finset.Set.hasCoeT.{u5} ι₂))) s₂))) -> (Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ p₂)))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u5}} (s : Finset.{u5} ι) {ι₂ : Type.{u3}} (s₂ : Finset.{u3} ι₂) {p : ι -> P}, (forall (i : ι), (Membership.mem.{u5, u5} ι (Finset.{u5} ι) (Finset.instMembershipFinset.{u5} ι) i s) -> (forall (j : ι), (Membership.mem.{u5, u5} ι (Finset.{u5} ι) (Finset.instMembershipFinset.{u5} ι) j s) -> (Eq.{succ u4} P (p i) (p j)) -> (Eq.{succ u5} ι i j))) -> (forall {p₂ : ι₂ -> P}, (forall (i : ι₂), (Membership.mem.{u3, u3} ι₂ (Finset.{u3} ι₂) (Finset.instMembershipFinset.{u3} ι₂) i s₂) -> (forall (j : ι₂), (Membership.mem.{u3, u3} ι₂ (Finset.{u3} ι₂) (Finset.instMembershipFinset.{u3} ι₂) j s₂) -> (Eq.{succ u4} P (p₂ i) (p₂ j)) -> (Eq.{succ u3} ι₂ i j))) -> (Eq.{succ u4} (Set.{u4} P) (Set.image.{u5, u4} ι P p (Finset.toSet.{u5} ι s)) (Set.image.{u3, u4} ι₂ P p₂ (Finset.toSet.{u3} ι₂ s₂))) -> (Eq.{succ u4} P (Finset.centroid.{u2, u1, u4, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u2, u1, u4, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ p₂)))
-Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eqₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
/-- Two indexed families of points that are injective on the given
@@ -1438,9 +1057,6 @@ variable {ι : Type _}
include V
-/- warning: weighted_vsub_mem_vector_span -> weightedVSub_mem_vectorSpan is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
@@ -1462,9 +1078,6 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
· exact fun _ => zero_smul k _
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
-/- warning: affine_combination_mem_affine_span -> affineCombination_mem_affineSpan is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
nontrivial. -/
@@ -1492,9 +1105,6 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
variable (k) {V}
-/- warning: mem_vector_span_iff_eq_weighted_vsub -> mem_vectorSpan_iff_eq_weightedVSub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
@@ -1540,9 +1150,6 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
variable {k}
-/- warning: eq_affine_combination_of_mem_affine_span -> eq_affineCombination_of_mem_affineSpan is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
@@ -1578,9 +1185,6 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
· rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
-/- warning: eq_affine_combination_of_mem_affine_span_of_fintype -> eq_affineCombination_of_mem_affineSpan_of_fintype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (w : ι → k)(hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
@@ -1594,9 +1198,6 @@ theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P}
variable (k V)
-/- warning: mem_affine_span_iff_eq_affine_combination -> mem_affineSpan_iff_eq_affineCombination is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
@@ -1610,9 +1211,6 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
exact affineCombination_mem_affineSpan hw p
#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombination
-/- warning: mem_affine_span_iff_eq_weighted_vsub_of_point_vadd -> mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
weights that are not required to sum to 1. -/
@@ -1640,9 +1238,6 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
variable {k V}
-/- warning: affine_span_eq_affine_span_line_map_units -> affineSpan_eq_affineSpan_lineMap_units is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_unitsₓ'. -/
/-- Given a set of points, together with a chosen base point in this set, if we affinely transport
all other members of the set along the line joining them to this base point, the affine span is
unchanged. -/
@@ -1672,12 +1267,6 @@ include V
open Set Finset
-/- warning: centroid_mem_affine_span_of_cast_card_ne_zero -> centroid_mem_affineSpan_of_cast_card_ne_zero is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u3} k (Nat.cast.{u3} k (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))))))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
-Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_cast_card_ne_zero centroid_mem_affineSpan_of_cast_card_ne_zeroₓ'. -/
/-- The centroid lies in the affine span if the number of points,
converted to `k`, is not zero. -/
theorem centroid_mem_affineSpan_of_cast_card_ne_zero {s : Finset ι} (p : ι → P)
@@ -1687,12 +1276,6 @@ theorem centroid_mem_affineSpan_of_cast_card_ne_zero {s : Finset ι} (p : ι →
variable (k)
-/- warning: centroid_mem_affine_span_of_card_ne_zero -> centroid_mem_affineSpan_of_card_ne_zero is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P), (Ne.{1} Nat (Finset.card.{u4} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P), (Ne.{1} Nat (Finset.card.{u3} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
-Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_card_ne_zero centroid_mem_affineSpan_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is not zero. -/
theorem centroid_mem_affineSpan_of_card_ne_zero [CharZero k] {s : Finset ι} (p : ι → P)
@@ -1700,12 +1283,6 @@ theorem centroid_mem_affineSpan_of_card_ne_zero [CharZero k] {s : Finset ι} (p
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_card_ne_zero k h) p
#align centroid_mem_affine_span_of_card_ne_zero centroid_mem_affineSpan_of_card_ne_zero
-/- warning: centroid_mem_affine_span_of_nonempty -> centroid_mem_affineSpan_of_nonempty is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P), (Finset.Nonempty.{u4} ι s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P), (Finset.Nonempty.{u3} ι s) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
-Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_nonempty centroid_mem_affineSpan_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the set is nonempty. -/
theorem centroid_mem_affineSpan_of_nonempty [CharZero k] {s : Finset ι} (p : ι → P)
@@ -1713,12 +1290,6 @@ theorem centroid_mem_affineSpan_of_nonempty [CharZero k] {s : Finset ι} (p : ι
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_nonempty k h) p
#align centroid_mem_affine_span_of_nonempty centroid_mem_affineSpan_of_nonempty
-/- warning: centroid_mem_affine_span_of_card_eq_add_one -> centroid_mem_affineSpan_of_card_eq_add_one is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P) {n : Nat}, (Eq.{1} Nat (Finset.card.{u4} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P) {n : Nat}, (Eq.{1} Nat (Finset.card.{u3} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
-Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_card_eq_add_one centroid_mem_affineSpan_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is `n + 1`. -/
theorem centroid_mem_affineSpan_of_card_eq_add_one [CharZero k] {s : Finset ι} (p : ι → P) {n : ℕ}
@@ -1736,12 +1307,6 @@ variable [affine_space V P] {ι : Type _} (s : Finset ι)
include V
-/- warning: affine_map.weighted_vsub_of_point -> AffineMap.weightedVSubOfPoint is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u4 u2, max u4 u3, u2, u2} k (Prod.{max u4 u2, u2} (ι -> V) V) (Prod.{max u4 u3, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.addCommGroup.{max u4 u2, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u4 u2, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u2} ι k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _inst_3) (Prod.addTorsor.{max u4 u2, max u4 u3, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.addTorsor.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
-but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (CommSemiring.toSemiring.{u1} k (CommRing.toCommSemiring.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.instAddTorsorForAllForAllAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
-Case conversion may be inaccurate. Consider using '#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPointₓ'. -/
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -62,10 +62,7 @@ lean 3 declaration is
but is expected to have type
Eq.{1} (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Insert.insert.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instInsertFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a b)) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Singleton.singleton.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instSingletonFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
Case conversion may be inaccurate. Consider using '#align finset.univ_fin2 Finset.univ_fin2ₓ'. -/
-theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} :=
- by
- ext x
- fin_cases x <;> simp
+theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} := by ext x; fin_cases x <;> simp
#align finset.univ_fin2 Finset.univ_fin2
variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
@@ -608,9 +605,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
let g₁ : s → V := fun i => w (f i) • (f i -ᵥ Classical.choice S.nonempty)
let g₂ : P → V := fun i => w i • (i -ᵥ Classical.choice S.nonempty)
change univ.sum g₁ = (image f univ).Sum g₂
- have hgf : g₁ = g₂ ∘ f := by
- ext
- simp
+ have hgf : g₁ = g₂ ∘ f := by ext; simp
rw [hgf, sum_image]
exact fun _ _ _ _ hxy => hf hxy
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
@@ -1214,12 +1209,8 @@ lean 3 declaration is
but is expected to have type
forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s)) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 P s (id.{succ u3} P))
Case conversion may be inaccurate. Consider using '#align finset.centroid_univ Finset.centroid_univₓ'. -/
-theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id :=
- by
- rw [centroid, centroid, ← s.attach_affine_combination_coe]
- congr
- ext
- simp
+theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id := by
+ rw [centroid, centroid, ← s.attach_affine_combination_coe]; congr ; ext; simp
#align finset.centroid_univ Finset.centroid_univ
/- warning: finset.centroid_singleton -> Finset.centroid_singleton is a dubious translation:
@@ -1456,8 +1447,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
(p : ι → P) : s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
classical
rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
- · skip
- simp [Finset.eq_empty_of_isEmpty s]
+ · skip; simp [Finset.eq_empty_of_isEmpty s]
· rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
Finsupp.mem_span_image_iff_total,
Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
@@ -1513,8 +1503,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
by
classical
constructor
- · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
- swap
+ · rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩); swap
· rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
Finsupp.mem_span_image_iff_total]
rintro ⟨l, hl, hv⟩
@@ -1642,9 +1631,7 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
by_cases hj : j ∈ s
· simp [Finset.sum_update_of_mem hj, Finset.insert_eq_of_mem hj]
· simp [w', Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
- have hww : ∀ i, i ≠ j → w i = w' i := by
- intro i hij
- simp [w', hij]
+ have hww : ∀ i, i ≠ j → w i = w' i := by intro i hij; simp [w', hij]
rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
s.weighted_vsub_of_point_insert w' p j, ←
(insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -91,10 +91,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
-/
/- warning: finset.weighted_vsub_of_point_apply -> Finset.weightedVSubOfPoint_apply is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -103,10 +100,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_apply
/- warning: finset.weighted_vsub_of_point_apply_const -> Finset.weightedVSubOfPoint_apply_const is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -116,10 +110,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_const
/- warning: finset.weighted_vsub_of_point_congr -> Finset.weightedVSubOfPoint_congr is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -133,10 +124,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congr
/- warning: finset.weighted_vsub_of_point_eq_of_weights_eq -> Finset.weightedVSubOfPoint_eq_of_weights_eq is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -153,10 +141,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eq
/- warning: finset.weighted_vsub_of_point_eq_of_sum_eq_zero -> Finset.weightedVSubOfPoint_eq_of_sum_eq_zero is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -174,10 +159,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zero
/- warning: finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one -> Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -198,10 +180,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one
/- warning: finset.weighted_vsub_of_point_erase -> Finset.weightedVSubOfPoint_erase is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -215,10 +194,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_erase
/- warning: finset.weighted_vsub_of_point_insert -> Finset.weightedVSubOfPoint_insert is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -232,10 +208,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insert
/- warning: finset.weighted_vsub_of_point_indicator_subset -> Finset.weightedVSubOfPoint_indicator_subset is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -249,10 +222,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
/- warning: finset.weighted_vsub_of_point_map -> Finset.weightedVSubOfPoint_map is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -265,10 +235,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_map
/- warning: finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -280,10 +247,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub
/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -293,10 +257,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub
/- warning: finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point -> Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -306,10 +267,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
/- warning: finset.weighted_vsub_of_point_sdiff -> Finset.weightedVSubOfPoint_sdiff is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -320,10 +278,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiff
/- warning: finset.weighted_vsub_of_point_sdiff_sub -> Finset.weightedVSubOfPoint_sdiff_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -334,10 +289,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_sub
/- warning: finset.weighted_vsub_of_point_subtype_eq_filter -> Finset.weightedVSubOfPoint_subtype_eq_filter is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -348,10 +300,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filter
/- warning: finset.weighted_vsub_of_point_filter_of_ne -> Finset.weightedVSubOfPoint_filter_of_ne is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -367,10 +316,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_ne
/- warning: finset.weighted_vsub_of_point_const_smul -> Finset.weightedVSubOfPoint_const_smul is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -407,10 +353,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
#align finset.weighted_vsub_apply Finset.weightedVSub_apply
/- warning: finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero -> Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -420,10 +363,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
/- warning: finset.weighted_vsub_apply_const -> Finset.weightedVSub_apply_const is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -446,10 +386,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
#align finset.weighted_vsub_empty Finset.weightedVSub_empty
/- warning: finset.weighted_vsub_congr -> Finset.weightedVSub_congr is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -459,10 +396,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
#align finset.weighted_vsub_congr Finset.weightedVSub_congr
/- warning: finset.weighted_vsub_indicator_subset -> Finset.weightedVSub_indicator_subset is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -472,10 +406,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subset
/- warning: finset.weighted_vsub_map -> Finset.weightedVSub_map is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -486,10 +417,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
#align finset.weighted_vsub_map Finset.weightedVSub_map
/- warning: finset.sum_smul_vsub_eq_weighted_vsub_sub -> Finset.sum_smul_vsub_eq_weightedVSub_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -499,10 +427,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_sub
/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub -> Finset.sum_smul_vsub_const_eq_weightedVSub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -512,10 +437,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
/- warning: finset.sum_smul_const_vsub_eq_neg_weighted_vsub -> Finset.sum_smul_const_vsub_eq_neg_weightedVSub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -525,10 +447,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
/- warning: finset.weighted_vsub_sdiff -> Finset.weightedVSub_sdiff is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -537,10 +456,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiff
/- warning: finset.weighted_vsub_sdiff_sub -> Finset.weightedVSub_sdiff_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -549,10 +465,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_sub
/- warning: finset.weighted_vsub_subtype_eq_filter -> Finset.weightedVSub_subtype_eq_filter is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -563,10 +476,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filter
/- warning: finset.weighted_vsub_filter_of_ne -> Finset.weightedVSub_filter_of_ne is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -576,10 +486,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_ne
/- warning: finset.weighted_vsub_const_smul -> Finset.weightedVSub_const_smul is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -625,10 +532,7 @@ theorem affineCombination_linear (p : ι → P) :
variable {k}
/- warning: finset.affine_combination_apply -> Finset.affineCombination_apply is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -644,10 +548,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
#align finset.affine_combination_apply Finset.affineCombination_apply
/- warning: finset.affine_combination_apply_const -> Finset.affineCombination_apply_const is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
@@ -657,10 +558,7 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
/- warning: finset.affine_combination_congr -> Finset.affineCombination_congr is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -670,10 +568,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
#align finset.affine_combination_congr Finset.affineCombination_congr
/- warning: finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one -> Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -684,10 +579,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
/- warning: finset.weighted_vsub_vadd_affine_combination -> Finset.weightedVSub_vadd_affineCombination is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
-but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -696,10 +588,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombination
/- warning: finset.affine_combination_vsub -> Finset.affineCombination_vsub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -708,10 +597,7 @@ theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
#align finset.affine_combination_vsub Finset.affineCombination_vsub
/- warning: finset.attach_affine_combination_of_injective -> Finset.attach_affineCombination_of_injective is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) -> P), (Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P f) -> (Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w f)) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
@@ -730,10 +616,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
/- warning: finset.attach_affine_combination_coe -> Finset.attach_affineCombination_coe is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (HasLiftT.mk.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (CoeTCₓ.coe.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeBase.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)))))))) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
@@ -758,10 +641,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combination
/- warning: finset.affine_combination_eq_linear_combination -> Finset.affineCombination_eq_linear_combination is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@@ -774,10 +654,7 @@ theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (
include S
/- warning: finset.affine_combination_of_eq_one_of_eq_zero -> Finset.affineCombination_of_eq_one_of_eq_zero is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@@ -797,10 +674,7 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zero
/- warning: finset.affine_combination_indicator_subset -> Finset.affineCombination_indicator_subset is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -812,10 +686,7 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subset
/- warning: finset.affine_combination_map -> Finset.affineCombination_map is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2) (succ u3), max (succ (max u5 u1)) (succ u3)} (AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι₂ -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
@@ -826,10 +697,7 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
#align finset.affine_combination_map Finset.affineCombination_map
/- warning: finset.sum_smul_vsub_eq_affine_combination_vsub -> Finset.sum_smul_vsub_eq_affineCombination_vsub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
@@ -841,10 +709,7 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsub
/- warning: finset.sum_smul_vsub_const_eq_affine_combination_vsub -> Finset.sum_smul_vsub_const_eq_affineCombination_vsub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
@@ -854,10 +719,7 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
/- warning: finset.sum_smul_const_vsub_eq_vsub_affine_combination -> Finset.sum_smul_const_vsub_eq_vsub_affineCombination is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
@@ -867,10 +729,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
/- warning: finset.affine_combination_sdiff_sub -> Finset.affineCombination_sdiff_sub is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -882,10 +741,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_sub
/- warning: finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one -> Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -903,10 +759,7 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
/- warning: finset.affine_combination_subtype_eq_filter -> Finset.affineCombination_subtype_eq_filter is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u4} ι pred) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -918,10 +771,7 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filter
/- warning: finset.affine_combination_filter_of_ne -> Finset.affineCombination_filter_of_ne is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
@@ -935,10 +785,7 @@ theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι
variable {V}
/- warning: finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype -> Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -969,10 +816,7 @@ theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V}
variable (k)
/- warning: finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype -> Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
-but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -991,10 +835,7 @@ theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι}
variable (V)
/- warning: finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype -> Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
-but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
@@ -1017,10 +858,7 @@ theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s
variable {k V}
/- warning: finset.map_affine_combination -> Finset.map_affineCombination is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
-but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
@@ -1216,10 +1054,7 @@ include S
variable (k)
/- warning: finset.affine_combination_affine_combination_single_weights -> Finset.affineCombination_affineCombinationSingleWeights is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
@@ -1232,10 +1067,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeights
/- warning: finset.weighted_vsub_weighted_vsub_vsub_weights -> Finset.weightedVSub_weightedVSubVSubWeights is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1250,10 +1082,7 @@ theorem weightedVSub_weightedVSubVSubWeights [DecidableEq ι] (p : ι → P) {i
variable {k}
/- warning: finset.affine_combination_affine_combination_line_map_weights -> Finset.affineCombination_affineCombinationLineMapWeights is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@@ -1372,10 +1201,7 @@ def centroid (p : ι → P) : P :=
-/
/- warning: finset.centroid_def -> Finset.centroid_def is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u1, u4} k _inst_1 ι s))
-but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
@@ -1542,10 +1368,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fin
include V
/- warning: finset.centroid_eq_affine_combination_fintype -> Finset.centroid_eq_affineCombination_fintype is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u1, u4} k _inst_1 ι s))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
+<too large>
Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
@@ -1625,10 +1448,7 @@ variable {ι : Type _}
include V
/- warning: weighted_vsub_mem_vector_span -> weightedVSub_mem_vectorSpan is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+<too large>
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1653,10 +1473,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
/- warning: affine_combination_mem_affine_span -> affineCombination_mem_affineSpan is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+<too large>
Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
@@ -1686,10 +1503,7 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
variable (k) {V}
/- warning: mem_vector_span_iff_eq_weighted_vsub -> mem_vectorSpan_iff_eq_weightedVSub is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
-but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1738,10 +1552,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
variable {k}
/- warning: eq_affine_combination_of_mem_affine_span -> eq_affineCombination_of_mem_affineSpan is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
@@ -1779,10 +1590,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
/- warning: eq_affine_combination_of_mem_affine_span_of_fintype -> eq_affineCombination_of_mem_affineSpan_of_fintype is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
-but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+<too large>
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
@@ -1798,10 +1606,7 @@ theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P}
variable (k V)
/- warning: mem_affine_span_iff_eq_affine_combination -> mem_affineSpan_iff_eq_affineCombination is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
-but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
@@ -1817,10 +1622,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombination
/- warning: mem_affine_span_iff_eq_weighted_vsub_of_point_vadd -> mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd is a dubious translation:
-lean 3 declaration is
- forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
-but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
@@ -1852,10 +1654,7 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
variable {k V}
/- warning: affine_span_eq_affine_span_line_map_units -> affineSpan_eq_affineSpan_lineMap_units is a dubious translation:
-lean 3 declaration is
- forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Nontrivial.{u1} k] {s : Set.{u3} P} {p : P}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p s) -> (forall (w : (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) -> (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1))), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u3} P (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) (fun (q : coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) => coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x s))))) q)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (coeBase.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (Units.hasCoe.{u1} k (Ring.toMonoid.{u1} k _inst_1))))) (w q))))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
-but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Nontrivial.{u3} k] {s : Set.{u2} P} {p : P}, (Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) p s) -> (forall (w : (Set.Elem.{u2} P s) -> (Units.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))), Eq.{succ u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u2} P (Set.Elem.{u2} P s) (fun (q : Set.Elem.{u2} P s) => FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 p (Subtype.val.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) x s) q)) (Units.val.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (w q))))) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+<too large>
Case conversion may be inaccurate. Consider using '#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_unitsₓ'. -/
/-- Given a set of points, together with a chosen base point in this set, if we affinely transport
all other members of the set along the line joining them to this base point, the affine span is
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -94,7 +94,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -106,7 +106,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -119,7 +119,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -156,7 +156,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -177,7 +177,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -201,7 +201,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -218,7 +218,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -235,7 +235,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -252,7 +252,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -268,7 +268,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -283,7 +283,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -296,7 +296,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -309,7 +309,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -337,7 +337,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -351,7 +351,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -938,7 +938,7 @@ variable {V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1820,7 +1820,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
@@ -1870,7 +1870,7 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq⊢ <;>
obtain ⟨t, μ, rfl⟩ := hq <;>
use t <;>
- [use fun x => μ x * ↑(w x), use fun x => μ x * ↑(w x)⁻¹] <;>
+ [use fun x => μ x * ↑(w x);use fun x => μ x * ↑(w x)⁻¹] <;>
simp [smul_smul]
#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_units
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -94,7 +94,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -106,7 +106,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -119,7 +119,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -156,7 +156,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -177,7 +177,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -201,7 +201,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -218,7 +218,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -235,7 +235,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -252,7 +252,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -268,7 +268,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -283,7 +283,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -296,7 +296,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -309,7 +309,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -337,7 +337,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -351,7 +351,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -938,7 +938,7 @@ variable {V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1820,7 +1820,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -94,7 +94,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -106,7 +106,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -119,7 +119,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -156,7 +156,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -177,7 +177,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -201,7 +201,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -218,7 +218,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -235,7 +235,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -252,7 +252,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -268,7 +268,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -283,7 +283,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -296,7 +296,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -309,7 +309,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -337,7 +337,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -351,7 +351,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -593,7 +593,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S)
but is expected to have type
- forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u1 u4, max u1 u4, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S)
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u1 u4, max u1 u4, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination Finset.affineCombinationₓ'. -/
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
@@ -612,7 +612,7 @@ def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u1} (ι -> k) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (AffineMap.linear.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)
but is expected to have type
- forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> P), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u4 u2, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u2} (ι -> k) (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (AffineMap.linear.{u4, max u4 u2, max u4 u2, u3, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u2} k _inst_1 ι) _inst_2 _inst_3 S (Finset.affineCombination.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)
+ forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> P), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u4 u2, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u2} (ι -> k) (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (AffineMap.linear.{u4, max u4 u2, max u4 u2, u3, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u2} k _inst_1 ι) _inst_2 _inst_3 S (Finset.affineCombination.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_linear Finset.affineCombination_linearₓ'. -/
/-- The linear map corresponding to `affine_combination` is
`weighted_vsub`. -/
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -647,7 +647,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
@@ -660,7 +660,7 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -711,7 +711,7 @@ theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) -> P), (Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P f) -> (Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w f)) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
@@ -733,7 +733,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (HasLiftT.mk.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (CoeTCₓ.coe.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeBase.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)))))))) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -761,7 +761,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@@ -777,7 +777,7 @@ include S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@@ -800,7 +800,7 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -815,7 +815,7 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2) (succ u3), max (succ (max u5 u1)) (succ u3)} (AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι₂ -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
@@ -829,7 +829,7 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
@@ -844,7 +844,7 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
@@ -857,7 +857,7 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -906,7 +906,7 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u4} ι pred) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -921,7 +921,7 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
@@ -938,7 +938,7 @@ variable {V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -994,7 +994,7 @@ variable (V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
@@ -1020,7 +1020,7 @@ variable {k V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
@@ -1219,7 +1219,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1253,7 +1253,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@@ -1375,7 +1375,7 @@ def centroid (p : ι → P) : P :=
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
@@ -1545,7 +1545,7 @@ include V
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1656,7 +1656,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1741,7 +1741,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
@@ -1782,7 +1782,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
@@ -1801,7 +1801,7 @@ variable (k V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
@@ -1820,7 +1820,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
@@ -1855,7 +1855,7 @@ variable {k V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Nontrivial.{u1} k] {s : Set.{u3} P} {p : P}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p s) -> (forall (w : (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) -> (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1))), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u3} P (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) (fun (q : coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) => coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x s))))) q)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (coeBase.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (Units.hasCoe.{u1} k (Ring.toMonoid.{u1} k _inst_1))))) (w q))))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Nontrivial.{u3} k] {s : Set.{u2} P} {p : P}, (Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) p s) -> (forall (w : (Set.Elem.{u2} P s) -> (Units.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))), Eq.{succ u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u2} P (Set.Elem.{u2} P s) (fun (q : Set.Elem.{u2} P s) => FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 p (Subtype.val.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) x s) q)) (Units.val.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (w q))))) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Nontrivial.{u3} k] {s : Set.{u2} P} {p : P}, (Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) p s) -> (forall (w : (Set.Elem.{u2} P s) -> (Units.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))), Eq.{succ u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u2} P (Set.Elem.{u2} P s) (fun (q : Set.Elem.{u2} P s) => FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 p (Subtype.val.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) x s) q)) (Units.val.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (w q))))) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
Case conversion may be inaccurate. Consider using '#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_unitsₓ'. -/
/-- Given a set of points, together with a chosen base point in this set, if we affinely transport
all other members of the set along the line joining them to this base point, the affine span is
@@ -1954,7 +1954,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u4 u2, max u4 u3, u2, u2} k (Prod.{max u4 u2, u2} (ι -> V) V) (Prod.{max u4 u3, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.addCommGroup.{max u4 u2, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u4 u2, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u2} ι k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _inst_3) (Prod.addTorsor.{max u4 u2, max u4 u3, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.addTorsor.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (CommSemiring.toSemiring.{u1} k (CommRing.toCommSemiring.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
+ forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (CommSemiring.toSemiring.{u1} k (CommRing.toCommSemiring.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.instAddTorsorForAllForAllAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
Case conversion may be inaccurate. Consider using '#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPointₓ'. -/
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -94,7 +94,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -106,7 +106,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -119,7 +119,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -156,7 +156,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -177,7 +177,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -201,7 +201,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -218,7 +218,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -235,7 +235,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -252,7 +252,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -268,7 +268,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -283,7 +283,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -296,7 +296,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -309,7 +309,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1988 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1987 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -337,7 +337,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -351,7 +351,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2310 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3314 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3313 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3533 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -647,7 +647,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
@@ -660,7 +660,7 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -711,7 +711,7 @@ theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) -> P), (Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P f) -> (Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w f)) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
@@ -733,7 +733,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (HasLiftT.mk.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (CoeTCₓ.coe.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeBase.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)))))))) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -761,7 +761,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@@ -777,7 +777,7 @@ include S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@@ -800,7 +800,7 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -815,7 +815,7 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2) (succ u3), max (succ (max u5 u1)) (succ u3)} (AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι₂ -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
@@ -829,7 +829,7 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
@@ -844,7 +844,7 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
@@ -857,7 +857,7 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -906,7 +906,7 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u4} ι pred) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -921,7 +921,7 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
@@ -938,7 +938,7 @@ variable {V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -994,7 +994,7 @@ variable (V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
@@ -1020,7 +1020,7 @@ variable {k V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
@@ -1094,7 +1094,7 @@ def weightedVSubVSubWeights [DecidableEq ι] (i j : ι) : ι → k :=
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u2 u1} (ι -> k) 0 (OfNat.mk.{max u2 u1} (ι -> k) 0 (Zero.zero.{max u2 u1} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7166 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7165 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_selfₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSubWeights k i i = 0 :=
@@ -1219,7 +1219,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1253,7 +1253,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@@ -1375,7 +1375,7 @@ def centroid (p : ι → P) : P :=
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
@@ -1545,7 +1545,7 @@ include V
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1656,7 +1656,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1741,7 +1741,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
@@ -1782,7 +1782,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
@@ -1801,7 +1801,7 @@ variable (k V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
@@ -1820,7 +1820,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.218 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -94,7 +94,7 @@ def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
@@ -106,7 +106,7 @@ theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
@@ -119,7 +119,7 @@ theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -136,7 +136,7 @@ theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
@@ -156,7 +156,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
@@ -177,7 +177,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
@@ -201,7 +201,7 @@ theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@@ -218,7 +218,7 @@ theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@@ -235,7 +235,7 @@ theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -252,7 +252,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
@@ -268,7 +268,7 @@ theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
@@ -283,7 +283,7 @@ theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -296,7 +296,7 @@ theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
@@ -309,7 +309,7 @@ theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1988 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1988 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -337,7 +337,7 @@ theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
@@ -351,7 +351,7 @@ theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3314 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3314 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -647,7 +647,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -761,7 +761,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@@ -777,7 +777,7 @@ include S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@@ -844,7 +844,7 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
@@ -857,7 +857,7 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -938,7 +938,7 @@ variable {V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -994,7 +994,7 @@ variable (V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
@@ -1020,7 +1020,7 @@ variable {k V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
@@ -1051,7 +1051,7 @@ def affineCombinationSingleWeights [DecidableEq ι] (i : ι) : ι → k :=
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1))))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_selfₓ'. -/
@[simp]
theorem affineCombinationSingleWeights_apply_self [DecidableEq ι] (i : ι) :
@@ -1073,7 +1073,7 @@ theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
@@ -1105,7 +1105,7 @@ theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSu
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_leftₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) :
@@ -1116,7 +1116,7 @@ theorem weightedVSubVSubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (Ring.toNeg.{u1} k _inst_1) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (Ring.toNeg.{u1} k _inst_1) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_rightₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) :
@@ -1169,7 +1169,7 @@ theorem affineCombinationLineMapWeights_self [DecidableEq ι] (i : ι) (c : k) :
lean 3 declaration is
forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) c))
but is expected to have type
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (Ring.toSub.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) c))
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (Ring.toSub.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) c))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_line_map_weights_apply_left Finset.affineCombinationLineMapWeights_apply_leftₓ'. -/
@[simp]
theorem affineCombinationLineMapWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) (c : k) :
@@ -1201,7 +1201,7 @@ theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι
lean 3 declaration is
forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
but is expected to have type
- forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (Ring.toSemiring.{u1} k _inst_1)))))
Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_line_map_weights Finset.sum_affineCombinationLineMapWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1287,7 +1287,7 @@ def centroidWeights : ι → k :=
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) (i : ι), Eq.{succ u1} k (Finset.centroidWeights.{u1, u2} k _inst_1 ι s i) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) (i : ι), Eq.{succ u2} k (Finset.centroidWeights.{u2, u1} k _inst_1 ι s i) (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s)))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) (i : ι), Eq.{succ u2} k (Finset.centroidWeights.{u2, u1} k _inst_1 ι s i) (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s)))
Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_apply Finset.centroidWeights_applyₓ'. -/
/-- `centroid_weights` at any point. -/
@[simp]
@@ -1299,7 +1299,7 @@ theorem centroidWeights_apply (i : ι) : s.centroidWeights k i = (card s : k)⁻
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u1, u2} k _inst_1 ι s) (Function.const.{succ u1, succ u2} k ι (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s) (Function.const.{succ u2, succ u1} k ι (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s) (Function.const.{succ u2, succ u1} k ι (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s))))
Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_eq_const Finset.centroidWeights_eq_constₓ'. -/
/-- `centroid_weights` equals a constant function. -/
theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card s : k)⁻¹ :=
@@ -1312,7 +1312,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall {k : Type.{u2}} [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), (Ne.{succ u2} k (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall {k : Type.{u2}} [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), (Ne.{succ u2} k (Nat.cast.{u2} k (Semiring.toNatCast.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))) (Finset.card.{u1} ι s)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zeroₓ'. -/
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
@@ -1326,7 +1326,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
@@ -1338,7 +1338,7 @@ theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
@@ -1351,7 +1351,7 @@ theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
@@ -1412,7 +1412,7 @@ theorem centroid_singleton (p : ι → P) (i : ι) : ({i} : Finset ι).centroid
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.hasSingleton.{u4} ι) i₂)) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.instSingletonFinset.{u4} ι) i₂)) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
+ forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.instSingletonFinset.{u4} ι) i₂)) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
Case conversion may be inaccurate. Consider using '#align finset.centroid_pair Finset.centroid_pairₓ'. -/
/-- The centroid of two points, expressed directly as adding a vector
to a point. -/
@@ -1436,7 +1436,7 @@ theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> P), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+ forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> P), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
Case conversion may be inaccurate. Consider using '#align finset.centroid_pair_fin Finset.centroid_pair_finₓ'. -/
/-- The centroid of two points indexed by `fin 2`, expressed directly
as adding a vector to the first point. -/
@@ -1497,7 +1497,7 @@ theorem sum_centroidWeightsIndicator [Fintype ι] :
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is not
@@ -1513,7 +1513,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the set is nonempty. -/
@@ -1528,7 +1528,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is `n + 1`. -/
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1656,7 +1656,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1741,7 +1741,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
@@ -1782,7 +1782,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
@@ -1801,7 +1801,7 @@ variable (k V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
@@ -1820,7 +1820,7 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
@@ -1890,7 +1890,7 @@ open Set Finset
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u3} k (Nat.cast.{u3} k (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))))))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u3} k (Nat.cast.{u3} k (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))))))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_cast_card_ne_zero centroid_mem_affineSpan_of_cast_card_ne_zeroₓ'. -/
/-- The centroid lies in the affine span if the number of points,
converted to `k`, is not zero. -/
@@ -1954,7 +1954,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u4 u2, max u4 u3, u2, u2} k (Prod.{max u4 u2, u2} (ι -> V) V) (Prod.{max u4 u3, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.addCommGroup.{max u4 u2, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u4 u2, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u2} ι k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _inst_3) (Prod.addTorsor.{max u4 u2, max u4 u3, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.addTorsor.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
+ forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (CommSemiring.toSemiring.{u1} k (CommRing.toCommSemiring.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
Case conversion may be inaccurate. Consider using '#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPointₓ'. -/
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -323,7 +323,7 @@ theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1996 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1988 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -370,7 +370,7 @@ theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2319 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2319 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2311 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
@@ -393,7 +393,7 @@ def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
@@ -410,7 +410,7 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
@@ -423,7 +423,7 @@ theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@@ -437,7 +437,7 @@ theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) =
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
@@ -449,7 +449,7 @@ theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).wei
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
@@ -462,7 +462,7 @@ theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -475,7 +475,7 @@ theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
@@ -489,7 +489,7 @@ theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
@@ -502,7 +502,7 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
@@ -515,7 +515,7 @@ theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
@@ -528,7 +528,7 @@ theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
@@ -540,7 +540,7 @@ theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s)
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3324 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3314 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -552,7 +552,7 @@ theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -566,7 +566,7 @@ theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
@@ -579,7 +579,7 @@ theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3544 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3544 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3534 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
@@ -628,7 +628,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
@@ -647,7 +647,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
@@ -660,7 +660,7 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
@@ -673,7 +673,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
@@ -687,7 +687,7 @@ theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι →
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
@@ -699,7 +699,7 @@ theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
@@ -711,7 +711,7 @@ theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) -> P), (Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P f) -> (Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w f)) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
@@ -733,7 +733,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (HasLiftT.mk.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (CoeTCₓ.coe.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeBase.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)))))))) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
@@ -747,7 +747,7 @@ omit S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@@ -761,7 +761,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@@ -777,7 +777,7 @@ include S
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@@ -800,7 +800,7 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
@@ -815,7 +815,7 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2) (succ u3), max (succ (max u5 u1)) (succ u3)} (AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι₂ -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
@@ -829,7 +829,7 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
@@ -844,7 +844,7 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
@@ -857,7 +857,7 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
@@ -870,7 +870,7 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
@@ -885,7 +885,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
@@ -906,7 +906,7 @@ theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u4} ι pred) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
@@ -921,7 +921,7 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
@@ -972,7 +972,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
@@ -994,7 +994,7 @@ variable (V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
@@ -1020,7 +1020,7 @@ variable {k V}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
but is expected to have type
- forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
@@ -1094,7 +1094,7 @@ def weightedVSubVSubWeights [DecidableEq ι] (i j : ι) : ι → k :=
lean 3 declaration is
forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u2 u1} (ι -> k) 0 (OfNat.mk.{max u2 u1} (ι -> k) 0 (Zero.zero.{max u2 u1} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
but is expected to have type
- forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7190 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7166 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_selfₓ'. -/
@[simp]
theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSubWeights k i i = 0 :=
@@ -1219,7 +1219,7 @@ variable (k)
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
@@ -1235,7 +1235,7 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@@ -1253,7 +1253,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@@ -1375,7 +1375,7 @@ def centroid (p : ι → P) : P :=
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
@@ -1545,7 +1545,7 @@ include V
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u1, u4} k _inst_1 ι s))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
@@ -1628,7 +1628,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
@@ -1656,7 +1656,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
but is expected to have type
- forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
@@ -1689,7 +1689,7 @@ variable (k) {V}
lean 3 declaration is
forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
@@ -1741,7 +1741,7 @@ variable {k}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
@@ -1782,7 +1782,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
but is expected to have type
- forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
@@ -1801,7 +1801,7 @@ variable (k V)
lean 3 declaration is
forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
but is expected to have type
- forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a
@@ -1954,7 +1954,7 @@ include V
lean 3 declaration is
forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u4 u2, max u4 u3, u2, u2} k (Prod.{max u4 u2, u2} (ι -> V) V) (Prod.{max u4 u3, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.addCommGroup.{max u4 u2, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u4 u2, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u2} ι k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _inst_3) (Prod.addTorsor.{max u4 u2, max u4 u3, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.addTorsor.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
but is expected to have type
- forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{max u2 u4, max u3 u4, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
+ forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{u2, max u3 u4, u3, max u2 u4} V (ι -> P) P (ι -> V) (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
Case conversion may be inaccurate. Consider using '#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPointₓ'. -/
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -20,6 +20,9 @@ import Mathbin.Tactic.FinCases
/-!
# Affine combinations of points
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file defines affine combinations of points.
## Main definitions
mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9
@@ -53,6 +53,12 @@ open BigOperators Affine
namespace Finset
+/- warning: finset.univ_fin2 -> Finset.univ_fin2 is a dubious translation:
+lean 3 declaration is
+ Eq.{1} (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Insert.insert.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.hasInsert.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (b : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) a b)) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (Singleton.singleton.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (Finset.hasSingleton.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
+but is expected to have type
+ Eq.{1} (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Insert.insert.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instInsertFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a b)) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Singleton.singleton.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (Finset.instSingletonFinset.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align finset.univ_fin2 Finset.univ_fin2ₓ'. -/
theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} :=
by
ext x
@@ -69,58 +75,90 @@ variable {ι : Type _} (s : Finset ι)
variable {ι₂ : Type _} (s₂ : Finset ι₂)
+#print Finset.weightedVSubOfPoint /-
/-- A weighted sum of the results of subtracting a base point from the
given points, as a linear map on the weights. The main cases of
interest are where the sum of the weights is 0, in which case the sum
is independent of the choice of base point, and where the sum of the
weights is 1, in which case the sum added to the base point is
independent of the choice of base point. -/
-def weightedVsubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
+def weightedVSubOfPoint (p : ι → P) (b : P) : (ι → k) →ₗ[k] V :=
∑ i in s, (LinearMap.proj i : (ι → k) →ₗ[k] k).smul_right (p i -ᵥ b)
-#align finset.weighted_vsub_of_point Finset.weightedVsubOfPoint
+#align finset.weighted_vsub_of_point Finset.weightedVSubOfPoint
+-/
+/- warning: finset.weighted_vsub_of_point_apply -> Finset.weightedVSubOfPoint_apply is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) b)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) b)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_applyₓ'. -/
@[simp]
-theorem weightedVsubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
- s.weightedVsubOfPoint p b w = ∑ i in s, w i • (p i -ᵥ b) := by
+theorem weightedVSubOfPoint_apply (w : ι → k) (p : ι → P) (b : P) :
+ s.weightedVSubOfPoint p b w = ∑ i in s, w i • (p i -ᵥ b) := by
simp [weighted_vsub_of_point, LinearMap.sum_apply]
-#align finset.weighted_vsub_of_point_apply Finset.weightedVsubOfPoint_apply
-
+#align finset.weighted_vsub_of_point_apply Finset.weightedVSubOfPoint_apply
+
+/- warning: finset.weighted_vsub_of_point_apply_const -> Finset.weightedVSubOfPoint_apply_const is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p b))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P) (b : P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p) b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p b))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_constₓ'. -/
/-- The value of `weighted_vsub_of_point`, where the given points are equal. -/
@[simp]
-theorem weightedVsubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
- s.weightedVsubOfPoint (fun _ => p) b w = (∑ i in s, w i) • (p -ᵥ b) := by
+theorem weightedVSubOfPoint_apply_const (w : ι → k) (p : P) (b : P) :
+ s.weightedVSubOfPoint (fun _ => p) b w = (∑ i in s, w i) • (p -ᵥ b) := by
rw [weighted_vsub_of_point_apply, sum_smul]
-#align finset.weighted_vsub_of_point_apply_const Finset.weightedVsubOfPoint_apply_const
-
+#align finset.weighted_vsub_of_point_apply_const Finset.weightedVSubOfPoint_apply_const
+
+/- warning: finset.weighted_vsub_of_point_congr -> Finset.weightedVSubOfPoint_congr is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (forall (b : P), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w₂)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congrₓ'. -/
/-- `weighted_vsub_of_point` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
-theorem weightedVsubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
+theorem weightedVSubOfPoint_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
(hp : ∀ i ∈ s, p₁ i = p₂ i) (b : P) :
- s.weightedVsubOfPoint p₁ b w₁ = s.weightedVsubOfPoint p₂ b w₂ :=
+ s.weightedVSubOfPoint p₁ b w₁ = s.weightedVSubOfPoint p₂ b w₂ :=
by
simp_rw [weighted_vsub_of_point_apply]
convert sum_congr rfl fun i hi => _
rw [hw i hi, hp i hi]
-#align finset.weighted_vsub_of_point_congr Finset.weightedVsubOfPoint_congr
-
+#align finset.weighted_vsub_of_point_congr Finset.weightedVSubOfPoint_congr
+
+/- warning: finset.weighted_vsub_of_point_eq_of_weights_eq -> Finset.weightedVSubOfPoint_eq_of_weights_eq is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P) (j : ι) (w₁ : ι -> k) (w₂ : ι -> k), (forall (i : ι), (Ne.{succ u4} ι i j) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₁) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p j)) w₂))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eqₓ'. -/
/-- Given a family of points, if we use a member of the family as a base point, the
`weighted_vsub_of_point` does not depend on the value of the weights at this point. -/
-theorem weightedVsubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂ : ι → k)
+theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂ : ι → k)
(hw : ∀ i, i ≠ j → w₁ i = w₂ i) :
- s.weightedVsubOfPoint p (p j) w₁ = s.weightedVsubOfPoint p (p j) w₂ :=
+ s.weightedVSubOfPoint p (p j) w₁ = s.weightedVSubOfPoint p (p j) w₂ :=
by
- simp only [Finset.weightedVsubOfPoint_apply]
+ simp only [Finset.weightedVSubOfPoint_apply]
congr
ext i
cases' eq_or_ne i j with h h
· simp [h]
· simp [hw i h]
-#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVsubOfPoint_eq_of_weights_eq
-
+#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eq
+
+/- warning: finset.weighted_vsub_of_point_eq_of_sum_eq_zero -> Finset.weightedVSubOfPoint_eq_of_sum_eq_zero is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroₓ'. -/
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
-theorem weightedVsubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 0)
- (b₁ b₂ : P) : s.weightedVsubOfPoint p b₁ w = s.weightedVsubOfPoint p b₂ w :=
+theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 0)
+ (b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w = s.weightedVSubOfPoint p b₂ w :=
by
apply eq_of_sub_eq_zero
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← sum_sub_distrib]
@@ -130,12 +168,18 @@ theorem weightedVsubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
ext
rw [← smul_sub, vsub_sub_vsub_cancel_left]
rw [← sum_smul, h, zero_smul]
-#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVsubOfPoint_eq_of_sum_eq_zero
-
+#align finset.weighted_vsub_of_point_eq_of_sum_eq_zero Finset.weightedVSubOfPoint_eq_of_sum_eq_zero
+
+/- warning: finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one -> Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b₁ : P) (b₂ : P), Eq.{succ u2} P (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₁) w) b₁) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b₂) w) b₂))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneₓ'. -/
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
-theorem weightedVsubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 1)
- (b₁ b₂ : P) : s.weightedVsubOfPoint p b₁ w +ᵥ b₁ = s.weightedVsubOfPoint p b₂ w +ᵥ b₂ :=
+theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 1)
+ (b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w +ᵥ b₁ = s.weightedVSubOfPoint p b₂ w +ᵥ b₂ :=
by
erw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← @vsub_eq_zero_iff_eq V,
vadd_vsub_assoc, vsub_vadd_eq_vsub_sub, ← add_sub_assoc, add_comm, add_sub_assoc, ←
@@ -148,236 +192,406 @@ theorem weightedVsubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P)
ext
rw [← smul_sub, vsub_sub_vsub_cancel_left]
rw [← sum_smul, h, one_smul, vsub_add_vsub_cancel, vsub_self]
-#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVsubOfPoint_vadd_eq_of_sum_eq_one
-
+#align finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one
+
+/- warning: finset.weighted_vsub_of_point_erase -> Finset.weightedVSubOfPoint_erase is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.erase.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b) s i) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_eraseₓ'. -/
/-- The weighted sum is unaffected by removing the base point, if
present, from the set of points. -/
@[simp]
-theorem weightedVsubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P) (i : ι) :
- (s.eraseₓ i).weightedVsubOfPoint p (p i) w = s.weightedVsubOfPoint p (p i) w :=
+theorem weightedVSubOfPoint_erase [DecidableEq ι] (w : ι → k) (p : ι → P) (i : ι) :
+ (s.eraseₓ i).weightedVSubOfPoint p (p i) w = s.weightedVSubOfPoint p (p i) w :=
by
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply]
apply sum_erase
rw [vsub_self, smul_zero]
-#align finset.weighted_vsub_of_point_erase Finset.weightedVsubOfPoint_erase
-
+#align finset.weighted_vsub_of_point_erase Finset.weightedVSubOfPoint_erase
+
+/- warning: finset.weighted_vsub_of_point_insert -> Finset.weightedVSubOfPoint_insert is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (w : ι -> k) (p : ι -> P) (i : ι), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) i s) p (p i)) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (p i)) w)
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insertₓ'. -/
/-- The weighted sum is unaffected by adding the base point, whether
or not present, to the set of points. -/
@[simp]
-theorem weightedVsubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P) (i : ι) :
- (insert i s).weightedVsubOfPoint p (p i) w = s.weightedVsubOfPoint p (p i) w :=
+theorem weightedVSubOfPoint_insert [DecidableEq ι] (w : ι → k) (p : ι → P) (i : ι) :
+ (insert i s).weightedVSubOfPoint p (p i) w = s.weightedVSubOfPoint p (p i) w :=
by
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply]
apply sum_insert_zero
rw [vsub_self, smul_zero]
-#align finset.weighted_vsub_of_point_insert Finset.weightedVsubOfPoint_insert
-
+#align finset.weighted_vsub_of_point_insert Finset.weightedVSubOfPoint_insert
+
+/- warning: finset.weighted_vsub_of_point_indicator_subset -> Finset.weightedVSubOfPoint_indicator_subset is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) (b : P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
-theorem weightedVsubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b : P) {s₁ s₂ : Finset ι}
+theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b : P) {s₁ s₂ : Finset ι}
(h : s₁ ⊆ s₂) :
- s₁.weightedVsubOfPoint p b w = s₂.weightedVsubOfPoint p b (Set.indicator (↑s₁) w) :=
+ s₁.weightedVSubOfPoint p b w = s₂.weightedVSubOfPoint p b (Set.indicator (↑s₁) w) :=
by
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply]
exact
Set.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
-#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVsubOfPoint_indicator_subset
-
+#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
+
+/- warning: finset.weighted_vsub_of_point_map -> Finset.weightedVSubOfPoint_map is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)) b) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)) b) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_mapₓ'. -/
/-- A weighted sum, over the image of an embedding, equals a weighted
sum with the same points and weights over the original
`finset`. -/
-theorem weightedVsubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) (b : P) :
- (s₂.map e).weightedVsubOfPoint p b w = s₂.weightedVsubOfPoint (p ∘ e) b (w ∘ e) :=
+theorem weightedVSubOfPoint_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) (b : P) :
+ (s₂.map e).weightedVSubOfPoint p b w = s₂.weightedVSubOfPoint (p ∘ e) b (w ∘ e) :=
by
simp_rw [weighted_vsub_of_point_apply]
exact Finset.sum_map _ _ _
-#align finset.weighted_vsub_of_point_map Finset.weightedVsubOfPoint_map
-
+#align finset.weighted_vsub_of_point_map Finset.weightedVSubOfPoint_map
+
+/- warning: finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two
`weighted_vsub_of_point` expressions. -/
-theorem sum_smul_vsub_eq_weightedVsubOfPoint_sub (w : ι → k) (p₁ p₂ : ι → P) (b : P) :
+theorem sum_smul_vsub_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ p₂ : ι → P) (b : P) :
(∑ i in s, w i • (p₁ i -ᵥ p₂ i)) =
- s.weightedVsubOfPoint p₁ b w - s.weightedVsubOfPoint p₂ b w :=
+ s.weightedVSubOfPoint p₁ b w - s.weightedVSubOfPoint p₂ b w :=
by
simp_rw [weighted_vsub_of_point_apply, ← sum_sub_distrib, ← smul_sub, vsub_sub_vsub_cancel_right]
-#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVsubOfPoint_sub
-
+#align finset.sum_smul_vsub_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub
+
+/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub -> Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₂ b)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) p₂))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁ b) w) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₂ b)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_subₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
-theorem sum_smul_vsub_const_eq_weightedVsubOfPoint_sub (w : ι → k) (p₁ : ι → P) (p₂ b : P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVsubOfPoint p₁ b w - (∑ i in s, w i) • (p₂ -ᵥ b) :=
+theorem sum_smul_vsub_const_eq_weightedVSubOfPoint_sub (w : ι → k) (p₁ : ι → P) (p₂ b : P) :
+ (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSubOfPoint p₁ b w - (∑ i in s, w i) • (p₂ -ᵥ b) :=
by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
-#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVsubOfPoint_sub
-
+#align finset.sum_smul_vsub_const_eq_weighted_vsub_of_point_sub Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub
+
+/- warning: finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point -> Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ b)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P) (b : P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ (p₂ i)))) (HSub.hSub.{u4, u4, u4} V ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) V (instHSub.{u4} V (SubNegMonoid.toSub.{u4} V (AddGroup.toSubNegMonoid.{u4} V (AddCommGroup.toAddGroup.{u4} V _inst_2)))) (HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) p₁ b)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂ b) w))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPointₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant,
expressed as a subtraction involving a `weighted_vsub_of_point` expression. -/
-theorem sum_smul_const_vsub_eq_sub_weightedVsubOfPoint (w : ι → k) (p₂ : ι → P) (p₁ b : P) :
- (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = (∑ i in s, w i) • (p₁ -ᵥ b) - s.weightedVsubOfPoint p₂ b w :=
+theorem sum_smul_const_vsub_eq_sub_weightedVSubOfPoint (w : ι → k) (p₂ : ι → P) (p₁ b : P) :
+ (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = (∑ i in s, w i) • (p₁ -ᵥ b) - s.weightedVSubOfPoint p₂ b w :=
by rw [sum_smul_vsub_eq_weighted_vsub_of_point_sub, weighted_vsub_of_point_apply_const]
-#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVsubOfPoint
-
+#align finset.sum_smul_const_vsub_eq_sub_weighted_vsub_of_point Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint
+
+/- warning: finset.weighted_vsub_of_point_sdiff -> Finset.weightedVSubOfPoint_sdiff is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
-theorem weightedVsubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
+theorem weightedVSubOfPoint_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
- (s \ s₂).weightedVsubOfPoint p b w + s₂.weightedVsubOfPoint p b w =
- s.weightedVsubOfPoint p b w :=
+ (s \ s₂).weightedVSubOfPoint p b w + s₂.weightedVSubOfPoint p b w =
+ s.weightedVSubOfPoint p b w :=
by simp_rw [weighted_vsub_of_point_apply, sum_sdiff h]
-#align finset.weighted_vsub_of_point_sdiff Finset.weightedVsubOfPoint_sdiff
-
+#align finset.weighted_vsub_of_point_sdiff Finset.weightedVSubOfPoint_sdiff
+
+/- warning: finset.weighted_vsub_of_point_sdiff_sub -> Finset.weightedVSubOfPoint_sdiff_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P) (b : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.1996 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p b) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p b) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
-theorem weightedVsubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
+theorem weightedVSubOfPoint_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) (b : P) :
- (s \ s₂).weightedVsubOfPoint p b w - s₂.weightedVsubOfPoint p b (-w) =
- s.weightedVsubOfPoint p b w :=
+ (s \ s₂).weightedVSubOfPoint p b w - s₂.weightedVSubOfPoint p b (-w) =
+ s.weightedVSubOfPoint p b w :=
by rw [map_neg, sub_neg_eq_add, s.weighted_vsub_of_point_sdiff h]
-#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVsubOfPoint_sdiff_sub
-
+#align finset.weighted_vsub_of_point_sdiff_sub Finset.weightedVSubOfPoint_sdiff_sub
+
+/- warning: finset.weighted_vsub_of_point_subtype_eq_filter -> Finset.weightedVSubOfPoint_subtype_eq_filter is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i)) b) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i)) b) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSubOfPoint.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w)
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
-theorem weightedVsubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
+theorem weightedVSubOfPoint_subtype_eq_filter (w : ι → k) (p : ι → P) (b : P) (pred : ι → Prop)
[DecidablePred pred] :
- ((s.Subtype pred).weightedVsubOfPoint (fun i => p i) b fun i => w i) =
- (s.filterₓ pred).weightedVsubOfPoint p b w :=
+ ((s.Subtype pred).weightedVSubOfPoint (fun i => p i) b fun i => w i) =
+ (s.filterₓ pred).weightedVSubOfPoint p b w :=
by rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, ← sum_subtype_eq_sum_filter]
-#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVsubOfPoint_subtype_eq_filter
-
+#align finset.weighted_vsub_of_point_subtype_eq_filter Finset.weightedVSubOfPoint_subtype_eq_filter
+
+/- warning: finset.weighted_vsub_of_point_filter_of_ne -> Finset.weightedVSubOfPoint_filter_of_ne is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p b) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
-theorem weightedVsubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {pred : ι → Prop}
+theorem weightedVSubOfPoint_filter_of_ne (w : ι → k) (p : ι → P) (b : P) {pred : ι → Prop}
[DecidablePred pred] (h : ∀ i ∈ s, w i ≠ 0 → pred i) :
- (s.filterₓ pred).weightedVsubOfPoint p b w = s.weightedVsubOfPoint p b w :=
+ (s.filterₓ pred).weightedVSubOfPoint p b w = s.weightedVSubOfPoint p b w :=
by
rw [weighted_vsub_of_point_apply, weighted_vsub_of_point_apply, sum_filter_of_ne]
intro i hi hne
refine' h i hi _
intro hw
simpa [hw] using hne
-#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVsubOfPoint_filter_of_ne
-
+#align finset.weighted_vsub_of_point_filter_of_ne Finset.weightedVSubOfPoint_filter_of_ne
+
+/- warning: finset.weighted_vsub_of_point_const_smul -> Finset.weightedVSubOfPoint_const_smul is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (b : P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2319 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2319 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of_point` may be moved outside the
sum. -/
-theorem weightedVsubOfPoint_const_smul (w : ι → k) (p : ι → P) (b : P) (c : k) :
- s.weightedVsubOfPoint p b (c • w) = c • s.weightedVsubOfPoint p b w := by
+theorem weightedVSubOfPoint_const_smul (w : ι → k) (p : ι → P) (b : P) (c : k) :
+ s.weightedVSubOfPoint p b (c • w) = c • s.weightedVSubOfPoint p b w := by
simp_rw [weighted_vsub_of_point_apply, smul_sum, Pi.smul_apply, smul_smul, smul_eq_mul]
-#align finset.weighted_vsub_of_point_const_smul Finset.weightedVsubOfPoint_const_smul
+#align finset.weighted_vsub_of_point_const_smul Finset.weightedVSubOfPoint_const_smul
+#print Finset.weightedVSub /-
/-- A weighted sum of the results of subtracting a default base point
from the given points, as a linear map on the weights. This is
intended to be used when the sum of the weights is 0; that condition
is specified as a hypothesis on those lemmas that require it. -/
-def weightedVsub (p : ι → P) : (ι → k) →ₗ[k] V :=
- s.weightedVsubOfPoint p (Classical.choice S.Nonempty)
-#align finset.weighted_vsub Finset.weightedVsub
+def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
+ s.weightedVSubOfPoint p (Classical.choice S.Nonempty)
+#align finset.weighted_vsub Finset.weightedVSub
+-/
+/- warning: finset.weighted_vsub_apply -> Finset.weightedVSub_apply is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p i) (Classical.choice.{succ u1} P (AddTorsor.Nonempty.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S)))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply Finset.weightedVSub_applyₓ'. -/
/-- Applying `weighted_vsub` with given weights. This is for the case
where a result involving a default base point is OK (for example, when
that base point will cancel out later); a more typical use case for
`weighted_vsub` would involve selecting a preferred base point with
`weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero` and then
using `weighted_vsub_of_point_apply`. -/
-theorem weightedVsub_apply (w : ι → k) (p : ι → P) :
- s.weightedVsub p w = ∑ i in s, w i • (p i -ᵥ Classical.choice S.Nonempty) := by
+theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
+ s.weightedVSub p w = ∑ i in s, w i • (p i -ᵥ Classical.choice S.Nonempty) := by
simp [weighted_vsub, LinearMap.sum_apply]
-#align finset.weighted_vsub_apply Finset.weightedVsub_apply
-
+#align finset.weighted_vsub_apply Finset.weightedVSub_apply
+
+/- warning: finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero -> Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (b : P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (forall (b : P), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zeroₓ'. -/
/-- `weighted_vsub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
-theorem weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
- (h : (∑ i in s, w i) = 0) (b : P) : s.weightedVsub p w = s.weightedVsubOfPoint p b w :=
- s.weightedVsubOfPoint_eq_of_sum_eq_zero w p h _ _
-#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero
-
+theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
+ (h : (∑ i in s, w i) = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
+ s.weightedVSubOfPoint_eq_of_sum_eq_zero w p h _ _
+#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
+
+/- warning: finset.weighted_vsub_apply_const -> Finset.weightedVSub_apply_const is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_constₓ'. -/
/-- The value of `weighted_vsub`, where the given points are equal and the sum of the weights
is 0. -/
@[simp]
-theorem weightedVsub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 0) :
- s.weightedVsub (fun _ => p) w = 0 := by
+theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 0) :
+ s.weightedVSub (fun _ => p) w = 0 := by
rw [weighted_vsub, weighted_vsub_of_point_apply_const, h, zero_smul]
-#align finset.weighted_vsub_apply_const Finset.weightedVsub_apply_const
-
+#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_const
+
+/- warning: finset.weighted_vsub_empty -> Finset.weightedVSub_empty is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u4} (Finset.{u4} ι) (Finset.hasEmptyc.{u4} ι)) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (EmptyCollection.emptyCollection.{u3} (Finset.{u3} ι) (Finset.instEmptyCollectionFinset.{u3} ι)) p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_empty Finset.weightedVSub_emptyₓ'. -/
/-- The `weighted_vsub` for an empty set is 0. -/
@[simp]
-theorem weightedVsub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).weightedVsub p w = (0 : V) := by
+theorem weightedVSub_empty (w : ι → k) (p : ι → P) : (∅ : Finset ι).weightedVSub p w = (0 : V) := by
simp [weighted_vsub_apply]
-#align finset.weighted_vsub_empty Finset.weightedVsub_empty
-
+#align finset.weighted_vsub_empty Finset.weightedVSub_empty
+
+/- warning: finset.weighted_vsub_congr -> Finset.weightedVSub_congr is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_congr Finset.weightedVSub_congrₓ'. -/
/-- `weighted_vsub` gives equal results for two families of weights and two families of points
that are equal on `s`. -/
-theorem weightedVsub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
- (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.weightedVsub p₁ w₁ = s.weightedVsub p₂ w₂ :=
- s.weightedVsubOfPoint_congr hw hp _
-#align finset.weighted_vsub_congr Finset.weightedVsub_congr
-
+theorem weightedVSub_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
+ (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.weightedVSub p₁ w₁ = s.weightedVSub p₂ w₂ :=
+ s.weightedVSubOfPoint_congr hw hp _
+#align finset.weighted_vsub_congr Finset.weightedVSub_congr
+
+/- warning: finset.weighted_vsub_indicator_subset -> Finset.weightedVSub_indicator_subset is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subsetₓ'. -/
/-- The weighted sum is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
-theorem weightedVsub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι} (h : s₁ ⊆ s₂) :
- s₁.weightedVsub p w = s₂.weightedVsub p (Set.indicator (↑s₁) w) :=
- weightedVsubOfPoint_indicator_subset _ _ _ h
-#align finset.weighted_vsub_indicator_subset Finset.weightedVsub_indicator_subset
-
+theorem weightedVSub_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι} (h : s₁ ⊆ s₂) :
+ s₁.weightedVSub p w = s₂.weightedVSub p (Set.indicator (↑s₁) w) :=
+ weightedVSubOfPoint_indicator_subset _ _ _ h
+#align finset.weighted_vsub_indicator_subset Finset.weightedVSub_indicator_subset
+
+/- warning: finset.weighted_vsub_map -> Finset.weightedVSub_map is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2), max (succ (max u5 u1)) (succ u2)} (LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u5 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι₂ -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u5 u1, u2} k k (ι₂ -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u5, u1} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u5, u1, u1} ι₂ k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u5)) (succ u2), max (succ u5) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u5, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι₂ -> k) V (Pi.addCommMonoid.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι₂ -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u5 u2, u3} k k (ι₂ -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u5, u2} ι₂ (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_map Finset.weightedVSub_mapₓ'. -/
/-- A weighted subtraction, over the image of an embedding, equals a
weighted subtraction with the same points and weights over the
original `finset`. -/
-theorem weightedVsub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
- (s₂.map e).weightedVsub p w = s₂.weightedVsub (p ∘ e) (w ∘ e) :=
- s₂.weightedVsubOfPoint_map _ _ _ _
-#align finset.weighted_vsub_map Finset.weightedVsub_map
-
+theorem weightedVSub_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
+ (s₂.map e).weightedVSub p w = s₂.weightedVSub (p ∘ e) (w ∘ e) :=
+ s₂.weightedVSubOfPoint_map _ _ _ _
+#align finset.weighted_vsub_map Finset.weightedVSub_map
+
+/- warning: finset.sum_smul_vsub_eq_weighted_vsub_sub -> Finset.sum_smul_vsub_eq_weightedVSub_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (HSub.hSub.{u4, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_subₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `weighted_vsub`
expressions. -/
-theorem sum_smul_vsub_eq_weightedVsub_sub (w : ι → k) (p₁ p₂ : ι → P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.weightedVsub p₁ w - s.weightedVsub p₂ w :=
- s.sum_smul_vsub_eq_weightedVsubOfPoint_sub _ _ _ _
-#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVsub_sub
-
+theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P) :
+ (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.weightedVSub p₁ w - s.weightedVSub p₂ w :=
+ s.sum_smul_vsub_eq_weightedVSubOfPoint_sub _ _ _ _
+#align finset.sum_smul_vsub_eq_weighted_vsub_sub Finset.sum_smul_vsub_eq_weightedVSub_sub
+
+/- warning: finset.sum_smul_vsub_const_eq_weighted_vsub -> Finset.sum_smul_vsub_const_eq_weightedVSub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
-theorem sum_smul_vsub_const_eq_weightedVsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVsub p₁ w := by
+theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p₂ : P)
+ (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSub p₁ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, sub_zero]
-#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVsub
-
+#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
+
+/- warning: finset.sum_smul_const_vsub_eq_neg_weighted_vsub -> Finset.sum_smul_const_vsub_eq_neg_weightedVSub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} V (SubNegMonoid.toHasNeg.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (Neg.neg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toNeg.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u2} (LinearMap.{u4, u4, max u4 u3, u2} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u2} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
-theorem sum_smul_const_vsub_eq_neg_weightedVsub (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = -s.weightedVsub p₂ w := by
+theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P) (p₁ : P)
+ (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = -s.weightedVSub p₂ w := by
rw [sum_smul_vsub_eq_weighted_vsub_sub, s.weighted_vsub_apply_const _ _ h, zero_sub]
-#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVsub
-
+#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
+
+/- warning: finset.weighted_vsub_sdiff -> Finset.weightedVSub_sdiff is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HAdd.hAdd.{u2, u2, u2} V V V (instHAdd.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HAdd.hAdd.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddZeroClass.toAdd.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddMonoid.toAddZeroClass.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) w)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiffₓ'. -/
/-- A weighted sum may be split into such sums over two subsets. -/
-theorem weightedVsub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
- (s \ s₂).weightedVsub p w + s₂.weightedVsub p w = s.weightedVsub p w :=
- s.weightedVsubOfPoint_sdiff h _ _ _
-#align finset.weighted_vsub_sdiff Finset.weightedVsub_sdiff
-
+theorem weightedVSub_sdiff [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k) (p : ι → P) :
+ (s \ s₂).weightedVSub p w + s₂.weightedVSub p w = s.weightedVSub p w :=
+ s.weightedVSubOfPoint_sdiff h _ _ _
+#align finset.weighted_vsub_sdiff Finset.weightedVSub_sdiff
+
+/- warning: finset.weighted_vsub_sdiff_sub -> Finset.weightedVSub_sdiff_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (HSub.hSub.{u2, u2, u2} V V V (instHSub.{u2} V (SubNegMonoid.toHasSub.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (HSub.hSub.{u3, u3, u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3324 : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegMonoid.toSub.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u2 u4} (ι -> k) (Pi.instNeg.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u2} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of such sums over two subsets. -/
-theorem weightedVsub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
- (p : ι → P) : (s \ s₂).weightedVsub p w - s₂.weightedVsub p (-w) = s.weightedVsub p w :=
- s.weightedVsubOfPoint_sdiff_sub h _ _ _
-#align finset.weighted_vsub_sdiff_sub Finset.weightedVsub_sdiff_sub
-
+theorem weightedVSub_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
+ (p : ι → P) : (s \ s₂).weightedVSub p w - s₂.weightedVSub p (-w) = s.weightedVSub p w :=
+ s.weightedVSubOfPoint_sdiff_sub h _ _ _
+#align finset.weighted_vsub_sdiff_sub Finset.weightedVSub_sdiff_sub
+
+/- warning: finset.weighted_vsub_subtype_eq_filter -> Finset.weightedVSub_subtype_eq_filter is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((Subtype.{succ u4} ι pred) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) ((Subtype.{succ u4} ι pred) -> k) V (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Subtype.{succ u4} ι pred) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k ((Subtype.{succ u4} ι pred) -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} (Subtype.{succ u4} ι pred) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filterₓ'. -/
/-- A weighted sum over `s.subtype pred` equals one over `s.filter pred`. -/
-theorem weightedVsub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
+theorem weightedVSub_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
- ((s.Subtype pred).weightedVsub (fun i => p i) fun i => w i) =
- (s.filterₓ pred).weightedVsub p w :=
- s.weightedVsubOfPoint_subtype_eq_filter _ _ _ _
-#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVsub_subtype_eq_filter
-
+ ((s.Subtype pred).weightedVSub (fun i => p i) fun i => w i) =
+ (s.filterₓ pred).weightedVSub p w :=
+ s.weightedVSubOfPoint_subtype_eq_filter _ _ _ _
+#align finset.weighted_vsub_subtype_eq_filter Finset.weightedVSub_subtype_eq_filter
+
+/- warning: finset.weighted_vsub_filter_of_ne -> Finset.weightedVSub_filter_of_ne is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_neₓ'. -/
/-- A weighted sum over `s.filter pred` equals one over `s` if all the weights at indices in `s`
not satisfying `pred` are zero. -/
-theorem weightedVsub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop} [DecidablePred pred]
- (h : ∀ i ∈ s, w i ≠ 0 → pred i) : (s.filterₓ pred).weightedVsub p w = s.weightedVsub p w :=
- s.weightedVsubOfPoint_filter_of_ne _ _ _ h
-#align finset.weighted_vsub_filter_of_ne Finset.weightedVsub_filter_of_ne
-
+theorem weightedVSub_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop} [DecidablePred pred]
+ (h : ∀ i ∈ s, w i ≠ 0 → pred i) : (s.filterₓ pred).weightedVSub p w = s.weightedVSub p w :=
+ s.weightedVSubOfPoint_filter_of_ne _ _ _ h
+#align finset.weighted_vsub_filter_of_ne Finset.weightedVSub_filter_of_ne
+
+/- warning: finset.weighted_vsub_const_smul -> Finset.weightedVSub_const_smul is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (SMul.smul.{u1, max u4 u1} k (ι -> k) (Function.hasSMul.{u4, u1, u1} ι k k (Mul.toSMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) c w)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) c (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P) (c : k), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3544 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSMul.hSMul.{u3, max u3 u2, max u3 u2} k (ι -> k) (ι -> k) (instHSMul.{u3, max u3 u2} k (ι -> k) (Pi.instSMul.{u2, u3, u3} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3544 : ι) => k) (fun (i : ι) => SMulZeroClass.toSMul.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (SMulWithZero.toSMulZeroClass.{u3, u3} k k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (MulZeroClass.toSMulWithZero.{u3} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))))))) c w)) (HSMul.hSMul.{u3, u4, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (instHSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SMulZeroClass.toSMul.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (NegZeroClass.toZero.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubNegZeroMonoid.toNegZeroClass.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionMonoid.toSubNegZeroMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (SubtractionCommMonoid.toSubtractionMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toDivisionAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))))) (Module.toMulActionWithZero.{u3, u4} k ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_3))))) c (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u4} (LinearMap.{u3, u3, max u3 u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u4} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u4, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smulₓ'. -/
/-- A constant multiplier of the weights in `weighted_vsub_of` may be moved outside the sum. -/
-theorem weightedVsub_const_smul (w : ι → k) (p : ι → P) (c : k) :
- s.weightedVsub p (c • w) = c • s.weightedVsub p w :=
- s.weightedVsubOfPoint_const_smul _ _ _ _
-#align finset.weighted_vsub_const_smul Finset.weightedVsub_const_smul
+theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
+ s.weightedVSub p (c • w) = c • s.weightedVSub p w :=
+ s.weightedVSubOfPoint_const_smul _ _ _ _
+#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smul
variable (k)
+/- warning: finset.affine_combination -> Finset.affineCombination is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S)
+but is expected to have type
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> P) -> (AffineMap.{u1, max u1 u4, max u1 u4, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S)
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination Finset.affineCombinationₓ'. -/
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
the weights. This is intended to be used when the sum of the weights
@@ -386,21 +600,33 @@ points with the given weights; that condition is specified as a
hypothesis on those lemmas that require it. -/
def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
where
- toFun w := s.weightedVsubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty
- linear := s.weightedVsub p
+ toFun w := s.weightedVSubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty
+ linear := s.weightedVSub p
map_vadd' w₁ w₂ := by simp_rw [vadd_vadd, weighted_vsub, vadd_eq_add, LinearMap.map_add]
#align finset.affine_combination Finset.affineCombination
+/- warning: finset.affine_combination_linear -> Finset.affineCombination_linear is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u1} (ι -> k) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (AffineMap.linear.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p)
+but is expected to have type
+ forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (p : ι -> P), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u4 u2, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (AddCommGroup.toAddCommMonoid.{max u4 u2} (ι -> k) (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (AffineMap.linear.{u4, max u4 u2, max u4 u2, u3, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u2, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u2} k _inst_1 ι) _inst_2 _inst_3 S (Finset.affineCombination.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)) (Finset.weightedVSub.{u4, u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p)
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_linear Finset.affineCombination_linearₓ'. -/
/-- The linear map corresponding to `affine_combination` is
`weighted_vsub`. -/
@[simp]
theorem affineCombination_linear (p : ι → P) :
- (s.affineCombination k p).linear = s.weightedVsub p :=
+ (s.affineCombination k p).linear = s.weightedVSub p :=
rfl
#align finset.affine_combination_linear Finset.affineCombination_linear
variable {k}
+/- warning: finset.affine_combination_apply -> Finset.affineCombination_apply is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S))) w) (Classical.choice.{succ u3} P (AddTorsor.nonempty.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u2)) (succ u1)) (succ u4), succ (max u3 u2), succ u4} (AffineMap.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u2, max u3 u2, u1, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u2, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u2, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u2 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u2, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u2, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S))) w) (Classical.choice.{succ u4} P (AddTorsor.Nonempty.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) S)))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply Finset.affineCombination_applyₓ'. -/
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
when that base point will cancel out later); a more typical use case
@@ -410,10 +636,16 @@ point with
then using `weighted_vsub_of_point_apply`. -/
theorem affineCombination_apply (w : ι → k) (p : ι → P) :
s.affineCombination k p w =
- s.weightedVsubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty :=
+ s.weightedVSubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty :=
rfl
#align finset.affine_combination_apply Finset.affineCombination_apply
+/- warning: finset.affine_combination_apply_const -> Finset.affineCombination_apply_const is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s (fun (_x : ι) => p)) w) p)
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_apply_const Finset.affineCombination_apply_constₓ'. -/
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 1) :
@@ -421,6 +653,12 @@ theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w
rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
+/- warning: finset.affine_combination_congr -> Finset.affineCombination_congr is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (p₁ i) (p₂ i))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w₁ : ι -> k} {w₂ : ι -> k}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w₁ i) (w₂ i))) -> (forall {p₁ : ι -> P} {p₂ : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u2} P (p₁ i) (p₂ i))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w₁) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w₂)))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_congr Finset.affineCombination_congrₓ'. -/
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
@@ -428,26 +666,50 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
simp_rw [affine_combination_apply, s.weighted_vsub_of_point_congr hw hp]
#align finset.affine_combination_congr Finset.affineCombination_congr
+/- warning: finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one -> Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (b : P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p : ι -> P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (b : P), Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u1)) (succ u2), succ (max u4 u3), succ u2} (AffineMap.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) S))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u4), max (succ u3) (succ u4), succ u1} (LinearMap.{u4, u4, max u4 u3, u1} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u3 u4, u1} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u3, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSubOfPoint.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p b) w) b))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_oneₓ'. -/
/-- `affine_combination` gives the sum with any base point, when the
sum of the weights is 1. -/
-theorem affineCombination_eq_weightedVsubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
+theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
(h : (∑ i in s, w i) = 1) (b : P) :
- s.affineCombination k p w = s.weightedVsubOfPoint p b w +ᵥ b :=
- s.weightedVsubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
-#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVsubOfPoint_vadd_of_sum_eq_one
-
+ s.affineCombination k p w = s.weightedVSubOfPoint p b w +ᵥ b :=
+ s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
+#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
+
+/- warning: finset.weighted_vsub_vadd_affine_combination -> Finset.weightedVSub_vadd_affineCombination is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u3} P (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u4 u1} (ι -> k) (Pi.instAdd.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k _inst_1)))) w₁ w₂))
+but is expected to have type
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u2}} (s : Finset.{u2} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (HVAdd.hVAdd.{u3, u4, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (instHVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddAction.toVAdd.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2))) (AddTorsor.toAddAction.{u3, u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AddCommGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w₁) _inst_2) S))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u2, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u2 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ (max u1 u2)) (succ u3)) (succ u4), succ (max u1 u2), succ u4} (AffineMap.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u2, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u2} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u4, u2} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} (ι -> k) (ι -> k) (ι -> k) (instHAdd.{max u1 u2} (ι -> k) (Pi.instAdd.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Distrib.toAdd.{u1} k (NonUnitalNonAssocSemiring.toDistrib.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))) w₁ w₂))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombinationₓ'. -/
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
-theorem weightedVsub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
- s.weightedVsub p w₁ +ᵥ s.affineCombination k p w₂ = s.affineCombination k p (w₁ + w₂) := by
+theorem weightedVSub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
+ s.weightedVSub p w₁ +ᵥ s.affineCombination k p w₂ = s.affineCombination k p (w₁ + w₂) := by
rw [← vadd_eq_add, AffineMap.map_vadd, affine_combination_linear]
-#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVsub_vadd_affineCombination
-
+#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVSub_vadd_affineCombination
+
+/- warning: finset.affine_combination_vsub -> Finset.affineCombination_vsub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u4 u1, max u4 u1, max u4 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u4 u1} (ι -> k) (Pi.instSub.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) w₁ w₂))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k) (p : ι -> P), Eq.{succ u4} V (VSub.vsub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddTorsor.toVSub.{u4, u3} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₁) (FunLike.coe.{max (max (succ (max u2 u1)) (succ u4)) (succ u3), succ (max u2 u1), succ u3} (AffineMap.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u1, max u2 u1, u4, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) w₂)) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), max (succ u1) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u1, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u3, u1} k V P _inst_1 _inst_2 _inst_3 S ι s p) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ι -> k) (ι -> k) (ι -> k) (instHSub.{max u2 u1} (ι -> k) (Pi.instSub.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toSub.{u2} k _inst_1))) w₁ w₂))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_vsub Finset.affineCombination_vsubₓ'. -/
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
- s.affineCombination k p w₁ -ᵥ s.affineCombination k p w₂ = s.weightedVsub p (w₁ - w₂) := by
+ s.affineCombination k p w₁ -ᵥ s.affineCombination k p w₂ = s.weightedVSub p (w₁ - w₂) := by
rw [← AffineMap.linearMap_vsub, affine_combination_linear, vsub_eq_sub]
#align finset.affine_combination_vsub Finset.affineCombination_vsub
+/- warning: finset.attach_affine_combination_of_injective -> Finset.attach_affineCombination_of_injective is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) -> P), (Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P f) -> (Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w f)) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_4 : DecidableEq.{succ u3} P] (s : Finset.{u3} P) (w : P -> k) (f : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> P), (Function.Injective.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P f) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) f) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w f)) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P (Finset.image.{u3, u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P (fun (a : P) (b : P) => _inst_4 a b) f (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s))) (id.{succ u3} P)) w))
+Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injectiveₓ'. -/
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w :=
@@ -464,6 +726,12 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
exact fun _ _ _ _ hxy => hf hxy
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
+/- warning: finset.attach_affine_combination_coe -> Finset.attach_affineCombination_coe is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} P (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) (Finset.attach.{u3} P s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Function.comp.{succ u3, succ u3, succ u1} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P k w ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (HasLiftT.mk.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (CoeTCₓ.coe.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeBase.{succ u3, succ u3} (Subtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s)))))))) (coeFn.{max (succ (max u3 u1)) (succ u2) (succ u3), max (succ (max u3 u1)) (succ u3)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (P -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u1} P (fun (i : P) => k) (fun (i : P) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} P (fun (i : P) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : P) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : P) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} P (fun (i : P) => k) (fun (i : P) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : P) => k) (fun (i : P) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P) (w : P -> k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) (fun (_x : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) ((Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.attach.{u3} P s) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Function.comp.{succ u3, succ u3, succ u2} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) P k w (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)))) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u1)) (succ u3), succ (max u2 u3), succ u3} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (P -> k) (fun (_x : P -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u3} k (P -> k) (P -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} P (fun (i : P) => k) (fun (i : P) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} P (fun (i : P) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : P) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : P) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 P) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 S P s (id.{succ u3} P)) w)
+Case conversion may be inaccurate. Consider using '#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coeₓ'. -/
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
@@ -472,14 +740,26 @@ theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
omit S
+/- warning: finset.weighted_vsub_eq_linear_combination -> Finset.weightedVSub_eq_linear_combination is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u3, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> V}, (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s w) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, a `weighted_vsub` is just a linear
combination. -/
@[simp]
-theorem weightedVsub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {p : ι → V}
- (hw : s.Sum w = 0) : s.weightedVsub p w = ∑ i in s, w i • p i := by
+theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {p : ι → V}
+ (hw : s.Sum w = 0) : s.weightedVSub p w = ∑ i in s, w i • p i := by
simp [s.weighted_vsub_apply, vsub_eq_sub, smul_sub, ← Finset.sum_smul, hw]
-#align finset.weighted_vsub_eq_linear_combination Finset.weightedVsub_eq_linear_combination
-
+#align finset.weighted_vsub_eq_linear_combination Finset.weightedVSub_eq_linear_combination
+
+/- warning: finset.affine_combination_eq_linear_combination -> Finset.affineCombination_eq_linear_combination is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u3} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (fun (_x : AffineMap.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) => (ι -> k) -> V) (AffineMap.hasCoeToFun.{u1, max u3 u1, max u3 u1, u2, u2} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u3, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u3, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (Finset.affineCombination.{u1, u2, u2, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)) ι s p) w) (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (p i))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> V) (w : ι -> k), (Eq.{succ u2} k (Finset.sum.{u2, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) w) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => V) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u1, u1} k (ι -> k) (ι -> k) V V _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (Finset.affineCombination.{u2, u1, u1, u3} k V V _inst_1 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2)) ι s p) w) (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (w i) (p i))))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combinationₓ'. -/
/-- Viewing a module as an affine space modelled on itself, affine combinations are just linear
combinations. -/
@[simp]
@@ -490,6 +770,12 @@ theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (
include S
+/- warning: finset.affine_combination_of_eq_one_of_eq_zero -> Finset.affineCombination_of_eq_one_of_eq_zero is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (i2 : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u1} k (w i2) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (i2 : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i2 s) -> (Ne.{succ u4} ι i2 i) -> (Eq.{succ u3} k (w i2) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (p i))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zeroₓ'. -/
/-- An `affine_combination` equals a point if that point is in the set
and has weight 1 and the other points in the set have weight 0. -/
@[simp]
@@ -507,6 +793,12 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
· simp [hw0 i2 hi2 h]
#align finset.affine_combination_of_eq_one_of_eq_zero Finset.affineCombination_of_eq_one_of_eq_zero
+/- warning: finset.affine_combination_indicator_subset -> Finset.affineCombination_indicator_subset is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (w : ι -> k) (p : ι -> P) {s₁ : Finset.{u4} ι} {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₁ s₂) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₁ p) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Set.indicator.{u4, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (Finset.toSet.{u4} ι s₁) w)))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subsetₓ'. -/
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι}
@@ -516,6 +808,12 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
weighted_vsub_of_point_indicator_subset _ _ _ h]
#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subset
+/- warning: finset.affine_combination_map -> Finset.affineCombination_map is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (coeFn.{max (succ (max u5 u1)) (succ u2) (succ u3), max (succ (max u5 u1)) (succ u3)} (AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι₂ -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u5 u1, max u5 u1, u2, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι₂) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι₂) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u5, u1, u1} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι₂) => k) (fun (i : ι₂) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e))) (Function.comp.{succ u5, succ u4, succ u1} ι₂ ι k w (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (w : ι -> k) (p : ι -> P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) w) (FunLike.coe.{max (max (succ (max u2 u5)) (succ u1)) (succ u3), succ (max u2 u5), succ u3} (AffineMap.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (ι₂ -> k) (fun (_x : ι₂ -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι₂ -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u5, max u2 u5, u1, u3} k (ι₂ -> k) (ι₂ -> k) V P _inst_1 (Pi.addCommGroup.{u5, u2} ι₂ (fun (i : ι₂) => k) (fun (i : ι₂) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u5, u2, u2} ι₂ (fun (i : ι₂) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι₂) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι₂) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u5} k _inst_1 ι₂) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 S ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e))) (Function.comp.{succ u5, succ u4, succ u2} ι₂ ι k w (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_map Finset.affineCombination_mapₓ'. -/
/-- An affine combination, over the image of an embedding, equals an
affine combination with the same points and weights over the original
`finset`. -/
@@ -524,6 +822,12 @@ theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
simp_rw [affine_combination_apply, weighted_vsub_of_point_map]
#align finset.affine_combination_map Finset.affineCombination_map
+/- warning: finset.sum_smul_vsub_eq_affine_combination_vsub -> Finset.sum_smul_vsub_eq_affineCombination_vsub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : ι -> P), Eq.{succ u4} V (Finset.sum.{u4, u3} V ι (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u2, u4, u4} k V V (instHSMul.{u2, u4} k V (SMulZeroClass.toSMul.{u2, u4} k V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2))))) (Module.toMulActionWithZero.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u4, u1} V P (AddTorsor.toVSub.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (p₁ i) (p₂ i)))) (VSub.vsub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u4, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u4} V _inst_2) S) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
@@ -533,6 +837,12 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
#align finset.sum_smul_vsub_eq_affine_combination_vsub Finset.sum_smul_vsub_eq_affineCombination_vsub
+/- warning: finset.sum_smul_vsub_const_eq_affine_combination_vsub -> Finset.sum_smul_vsub_const_eq_affineCombination_vsub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₁ : ι -> P) (p₂ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p₁ i) p₂))) (VSub.vsub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u2, u1} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₁) w) p₂))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsubₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
@@ -540,6 +850,12 @@ theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
+/- warning: finset.sum_smul_const_vsub_eq_vsub_affine_combination -> Finset.sum_smul_const_vsub_eq_vsub_affineCombination is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u4} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (w i) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (w : ι -> k) (p₂ : ι -> P) (p₁ : P), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} V (Finset.sum.{u2, u3} V ι (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) s (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} k V V (instHSMul.{u4, u2} k V (SMulZeroClass.toSMul.{u4, u2} k V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u2} k V (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u2} k V (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))) (Module.toMulActionWithZero.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (w i) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (p₂ i)))) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) p₁ (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p₂) w)))
+Case conversion may be inaccurate. Consider using '#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombinationₓ'. -/
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
@@ -547,19 +863,31 @@ theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
+/- warning: finset.affine_combination_sdiff_sub -> Finset.affineCombination_sdiff_sub is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.hasSubset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u2} V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.hasSdiff.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u4 u1} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) w))) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u1, u3} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] {s₂ : Finset.{u4} ι}, (HasSubset.Subset.{u4} (Finset.{u4} ι) (Finset.instHasSubsetFinset.{u4} ι) s₂ s) -> (forall (w : ι -> k) (p : ι -> P), Eq.{succ u3} V (VSub.vsub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddTorsor.toVSub.{u3, u2} V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (SDiff.sdiff.{u4} (Finset.{u4} ι) (Finset.instSDiffFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_4 a b)) s s₂) p) w) (FunLike.coe.{max (max (succ (max u1 u4)) (succ u3)) (succ u2), succ (max u1 u4), succ u2} (AffineMap.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u1 u4, max u1 u4, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_1)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s₂ p) (Neg.neg.{max u1 u4} (ι -> k) (Pi.instNeg.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => Ring.toNeg.{u1} k _inst_1)) w))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u4) (succ u1), succ u3} (LinearMap.{u1, u1, max u1 u4, u3} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u4 u1, u3} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_1)) _inst_3 (RingHom.id.{u1} k (NonAssocRing.toNonAssocSemiring.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u3, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_subₓ'. -/
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) :
- (s \ s₂).affineCombination k p w -ᵥ s₂.affineCombination k p (-w) = s.weightedVsub p w :=
+ (s \ s₂).affineCombination k p w -ᵥ s₂.affineCombination k p (-w) = s.weightedVSub p w :=
by
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.weighted_vsub_sdiff_sub h _ _
#align finset.affine_combination_sdiff_sub Finset.affineCombination_sdiff_sub
+/- warning: finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one -> Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i)], (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι (fun (_x : ι) => Ne.{succ u4} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u4}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u4} V] [_inst_3 : Module.{u2, u4} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2)] [S : AddTorsor.{u4, u1} V P (AddCommGroup.toAddGroup.{u4} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {w : ι -> k} {p : ι -> P}, (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u3) (succ u2), succ u4} (LinearMap.{u2, u2, max u2 u3, u4} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u4} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} V _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w) (OfNat.ofNat.{u4} V 0 (Zero.toOfNat0.{u4} V (NegZeroClass.toZero.{u4} V (SubNegZeroMonoid.toNegZeroClass.{u4} V (SubtractionMonoid.toSubNegZeroMonoid.{u4} V (SubtractionCommMonoid.toSubtractionMonoid.{u4} V (AddCommGroup.toDivisionAddCommMonoid.{u4} V _inst_2)))))))) -> (forall {i : ι} [_inst_4 : DecidablePred.{succ u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i)], (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u2} k (w i) (Neg.neg.{u2} k (Ring.toNeg.{u2} k _inst_1) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u2 u3)) (succ u4)) (succ u1), succ (max u2 u3), succ u1} (AffineMap.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u3, max u2 u3, u4, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u3, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u4, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u3} ι (fun (_x : ι) => Ne.{succ u3} ι _x i) (fun (a : ι) => _inst_4 a) s) p) w) (p i)))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_oneₓ'. -/
/-- If a weighted sum is zero and one of the weights is `-1`, the corresponding point is
the affine combination of the other points with the given weights. -/
-theorem affineCombination_eq_of_weightedVsub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
- (hw : s.weightedVsub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
+theorem affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
+ (hw : s.weightedVSub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
(hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by
classical
rw [← @vsub_eq_zero_iff_eq V, ← hw, ←
@@ -569,8 +897,14 @@ theorem affineCombination_eq_of_weightedVsub_eq_zero_of_eq_neg_one {w : ι → k
refine' (affine_combination_of_eq_one_of_eq_zero _ _ _ (mem_singleton_self _) _ _).symm
· simp [hwi]
· simp
-#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVsub_eq_zero_of_eq_neg_one
-
+#align finset.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one
+
+/- warning: finset.affine_combination_subtype_eq_filter -> Finset.affineCombination_subtype_eq_filter is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((Subtype.{succ u4} ι pred) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (fun (i : Subtype.{succ u4} ι pred) => w ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Subtype.{succ u4} ι pred) ι (HasLiftT.mk.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (CoeTCₓ.coe.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeBase.{succ u4, succ u4} (Subtype.{succ u4} ι pred) ι (coeSubtype.{succ u4} ι (fun (x : ι) => pred x))))) i))) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) (pred : ι -> Prop) [_inst_4 : DecidablePred.{succ u4} ι pred], Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) ((Subtype.{succ u4} ι pred) -> k) (fun (_x : (Subtype.{succ u4} ι pred) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Subtype.{succ u4} ι pred) -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k ((Subtype.{succ u4} ι pred) -> k) ((Subtype.{succ u4} ι pred) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) (fun (i : Subtype.{succ u4} ι pred) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} (Subtype.{succ u4} ι pred) (fun (i : Subtype.{succ u4} ι pred) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : Subtype.{succ u4} ι pred) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : Subtype.{succ u4} ι pred) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 (Subtype.{succ u4} ι pred)) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (Subtype.{succ u4} ι pred) (Finset.subtype.{u4} ι pred (fun (a : ι) => _inst_4 a) s) (fun (i : Subtype.{succ u4} ι pred) => p (Subtype.val.{succ u4} ι pred i))) (fun (i : Subtype.{succ u4} ι pred) => w (Subtype.val.{succ u4} ι pred i))) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w)
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filterₓ'. -/
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
@@ -580,6 +914,12 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
rw [affine_combination_apply, affine_combination_apply, weighted_vsub_of_point_subtype_eq_filter]
#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filter
+/- warning: finset.affine_combination_filter_of_ne -> Finset.affineCombination_filter_of_ne is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Ne.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (pred i)) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (w : ι -> k) (p : ι -> P) {pred : ι -> Prop} [_inst_4 : DecidablePred.{succ u4} ι pred], (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Ne.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (pred i)) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι (Finset.filter.{u4} ι pred (fun (a : ι) => _inst_4 a) s) p) w) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_neₓ'. -/
/-- An affine combination over `s.filter pred` equals one over `s` if all the weights at indices
in `s` not satisfying `pred` are zero. -/
theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop}
@@ -591,6 +931,12 @@ theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι
variable {V}
+/- warning: finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype -> Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) x) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i)) b) w)))))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {x : k} {s : Set.{u4} ι} {p : ι -> P} {b : P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p b) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) x) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i)) b) w)))))
+Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as
`weighted_vsub_of_point` using a `finset` lying within that subset and
@@ -598,12 +944,12 @@ with a given sum of weights if and only if it can be expressed as
`weighted_vsub_of_point` with that sum of weights for the
corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
-theorem eq_weightedVsubOfPoint_subset_iff_eq_weightedVsubOfPoint_subtype {v : V} {x : k} {s : Set ι}
+theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V} {x : k} {s : Set ι}
{p : ι → P} {b : P} :
(∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = x),
- v = fs.weightedVsubOfPoint p b w) ↔
+ v = fs.weightedVSubOfPoint p b w) ↔
∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = x),
- v = fs.weightedVsubOfPoint (fun i : s => p i) b w :=
+ v = fs.weightedVSubOfPoint (fun i : s => p i) b w :=
by
classical
simp_rw [weighted_vsub_of_point_apply]
@@ -615,26 +961,38 @@ theorem eq_weightedVsubOfPoint_subset_iff_eq_weightedVsubOfPoint_subtype {v : V}
⟨fs.map (Function.Embedding.subtype _), map_subtype_subset _, fun i =>
if h : i ∈ s then w ⟨i, h⟩ else 0, _, _⟩ <;>
simp
-#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVsubOfPoint_subset_iff_eq_weightedVsubOfPoint_subtype
+#align finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
variable (k)
+/- warning: finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype -> Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
+but is expected to have type
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) => Eq.{succ u2} V v (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) ((Set.Elem.{u4} ι s) -> k) V (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : (Set.Elem.{u4} ι s) -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k ((Set.Elem.{u4} ι s) -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} (Set.Elem.{u4} ι s) (fun (ᾰ : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+Case conversion may be inaccurate. Consider using '#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A vector can be expressed as `weighted_vsub` using
a `finset` lying within that subset and with sum of weights 0 if and
only if it can be expressed as `weighted_vsub` with sum of weights 0
for the corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
-theorem eq_weightedVsub_subset_iff_eq_weightedVsub_subtype {v : V} {s : Set ι} {p : ι → P} :
+theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι} {p : ι → P} :
(∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = 0),
- v = fs.weightedVsub p w) ↔
+ v = fs.weightedVSub p w) ↔
∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = 0),
- v = fs.weightedVsub (fun i : s => p i) w :=
- eq_weightedVsubOfPoint_subset_iff_eq_weightedVsubOfPoint_subtype
-#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVsub_subset_iff_eq_weightedVsub_subtype
+ v = fs.weightedVSub (fun i : s => p i) w :=
+ eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
+#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
variable (V)
+/- warning: finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype -> Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.hasSubset.{u4} ι) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) fs) s) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) (fun (fs : Finset.{u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s)) => Exists.{max (succ u4) (succ u1)} ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) (fun (w : (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p0 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) ((coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => k) (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) fs (fun (i : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) => p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι) Type.{u4} (Set.hasCoeToSort.{u4} ι) s) ι (coeSubtype.{succ u4} ι (fun (x : ι) => Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) x s))))) i))) w)))))
+but is expected to have type
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p0 : P} {s : Set.{u4} ι} {p : ι -> P}, Iff (Exists.{succ u4} (Finset.{u4} ι) (fun (fs : Finset.{u4} ι) => Exists.{0} (HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) (fun (hfs : HasSubset.Subset.{u4} (Set.{u4} ι) (Set.instHasSubsetSet.{u4} ι) (Finset.toSet.{u4} ι fs) s) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S ι fs p) w)))))) (Exists.{succ u4} (Finset.{u4} (Set.Elem.{u4} ι s)) (fun (fs : Finset.{u4} (Set.Elem.{u4} ι s)) => Exists.{max (succ u3) (succ u4)} ((Set.Elem.{u4} ι s) -> k) (fun (w : (Set.Elem.{u4} ι s) -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k (Set.Elem.{u4} ι s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) fs (fun (i : Set.Elem.{u4} ι s) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p0 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) ((Set.Elem.{u4} ι s) -> k) (fun (_x : (Set.Elem.{u4} ι s) -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : (Set.Elem.{u4} ι s) -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k ((Set.Elem.{u4} ι s) -> k) ((Set.Elem.{u4} ι s) -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) (fun (i : Set.Elem.{u4} ι s) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} (Set.Elem.{u4} ι s) (fun (i : Set.Elem.{u4} ι s) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : Set.Elem.{u4} ι s) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : Set.Elem.{u4} ι s) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 (Set.Elem.{u4} ι s)) _inst_2 _inst_3 S) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 S (Set.Elem.{u4} ι s) fs (fun (i : Set.Elem.{u4} ι s) => p (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) i))) w)))))
+Case conversion may be inaccurate. Consider using '#align finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtypeₓ'. -/
/-- Suppose an indexed family of points is given, along with a subset
of the index type. A point can be expressed as an
`affine_combination` using a `finset` lying within that subset and
@@ -655,6 +1013,12 @@ theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s
variable {k V}
+/- warning: finset.map_affine_combination -> Finset.map_affineCombination is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_4 : AddCommGroup.{u5} V₂] [_inst_5 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_4)] [_inst_6 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s w) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u6} P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (coeFn.{max (succ (max u4 u1)) (succ u5) (succ u6), max (succ (max u4 u1)) (succ u6)} (AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) => (ι -> k) -> P₂) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u5, u6} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+but is expected to have type
+ forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) {V₂ : Type.{u6}} {P₂ : Type.{u5}} [_inst_4 : AddCommGroup.{u6} V₂] [_inst_5 : Module.{u4, u6} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₂ _inst_4)] [_inst_6 : AddTorsor.{u6, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u6} V₂ _inst_4)] (p : ι -> P) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u3} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s w) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (forall (f : AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6), Eq.{succ u5} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u4, u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S ι s p) w)) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u6)) (succ u5), succ (max u4 u3), succ u5} (AffineMap.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P₂) _x) (AffineMap.funLike.{u4, max u4 u3, max u4 u3, u6, u5} k (ι -> k) (ι -> k) V₂ P₂ _inst_1 (Pi.addCommGroup.{u3, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u3, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u3} k _inst_1 ι) _inst_4 _inst_5 _inst_6) (Finset.affineCombination.{u4, u6, u5, u3} k V₂ P₂ _inst_1 _inst_4 _inst_5 _inst_6 ι s (Function.comp.{succ u3, succ u1, succ u5} ι P P₂ (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u6)) (succ u5), succ u1, succ u5} (AffineMap.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u4, u2, u1, u6, u5} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 S _inst_4 _inst_5 _inst_6) f) p)) w))
+Case conversion may be inaccurate. Consider using '#align finset.map_affine_combination Finset.map_affineCombinationₓ'. -/
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.Sum w = 1) (f : P →ᵃ[k] P₂) :
@@ -673,21 +1037,41 @@ variable (k)
omit S
+#print Finset.affineCombinationSingleWeights /-
/-- Weights for expressing a single point as an affine combination. -/
def affineCombinationSingleWeights [DecidableEq ι] (i : ι) : ι → k :=
Function.update (Function.const ι 0) i 1
#align finset.affine_combination_single_weights Finset.affineCombinationSingleWeights
+-/
+/- warning: finset.affine_combination_single_weights_apply_self -> Finset.affineCombinationSingleWeights_apply_self is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_selfₓ'. -/
@[simp]
theorem affineCombinationSingleWeights_apply_self [DecidableEq ι] (i : ι) :
affineCombinationSingleWeights k i i = 1 := by simp [affine_combination_single_weights]
#align finset.affine_combination_single_weights_apply_self Finset.affineCombinationSingleWeights_apply_self
+/- warning: finset.affine_combination_single_weights_apply_of_ne -> Finset.affineCombinationSingleWeights_apply_of_ne is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι j i) -> (Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι j i) -> (Eq.{succ u1} k (Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_single_weights_apply_of_ne Finset.affineCombinationSingleWeights_apply_of_neₓ'. -/
@[simp]
theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (h : j ≠ i) :
affineCombinationSingleWeights k i j = 0 := by simp [affine_combination_single_weights, h]
#align finset.affine_combination_single_weights_apply_of_ne Finset.affineCombinationSingleWeights_apply_of_ne
+/- warning: finset.sum_affine_combination_single_weights -> Finset.sum_affineCombinationSingleWeights is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (j : ι) => Finset.affineCombinationSingleWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
(∑ j in s, affineCombinationSingleWeights k i j) = 1 :=
@@ -696,70 +1080,126 @@ theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈
exact sum_eq_single_of_mem i h fun j _ hj => affine_combination_single_weights_apply_of_ne k hj
#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeights
+#print Finset.weightedVSubVSubWeights /-
/-- Weights for expressing the subtraction of two points as a `weighted_vsub`. -/
-def weightedVsubVsubWeights [DecidableEq ι] (i j : ι) : ι → k :=
+def weightedVSubVSubWeights [DecidableEq ι] (i j : ι) : ι → k :=
affineCombinationSingleWeights k i - affineCombinationSingleWeights k j
-#align finset.weighted_vsub_vsub_weights Finset.weightedVsubVsubWeights
+#align finset.weighted_vsub_vsub_weights Finset.weightedVSubVSubWeights
+-/
+/- warning: finset.weighted_vsub_vsub_weights_self -> Finset.weightedVSubVSubWeights_self is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u2 u1} (ι -> k) 0 (OfNat.mk.{max u2 u1} (ι -> k) 0 (Zero.zero.{max u2 u1} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u1) (succ u2)} (ι -> k) (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i i) (OfNat.ofNat.{max u1 u2} (ι -> k) 0 (Zero.toOfNat0.{max u1 u2} (ι -> k) (Pi.instZero.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.7190 : ι) => k) (fun (i : ι) => MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_selfₓ'. -/
@[simp]
-theorem weightedVsubVsubWeights_self [DecidableEq ι] (i : ι) : weightedVsubVsubWeights k i i = 0 :=
+theorem weightedVSubVSubWeights_self [DecidableEq ι] (i : ι) : weightedVSubVSubWeights k i i = 0 :=
by simp [weighted_vsub_vsub_weights]
-#align finset.weighted_vsub_vsub_weights_self Finset.weightedVsubVsubWeights_self
-
+#align finset.weighted_vsub_vsub_weights_self Finset.weightedVSubVSubWeights_self
+
+/- warning: finset.weighted_vsub_vsub_weights_apply_left -> Finset.weightedVSubVSubWeights_apply_left is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j i) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_leftₓ'. -/
@[simp]
-theorem weightedVsubVsubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) :
- weightedVsubVsubWeights k i j i = 1 := by simp [weighted_vsub_vsub_weights, h]
-#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVsubVsubWeights_apply_left
-
+theorem weightedVSubVSubWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) :
+ weightedVSubVSubWeights k i j i = 1 := by simp [weighted_vsub_vsub_weights, h]
+#align finset.weighted_vsub_vsub_weights_apply_left Finset.weightedVSubVSubWeights_apply_left
+
+/- warning: finset.weighted_vsub_vsub_weights_apply_right -> Finset.weightedVSubVSubWeights_apply_right is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (SubNegMonoid.toHasNeg.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j j) (Neg.neg.{u1} k (Ring.toNeg.{u1} k _inst_1) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_rightₓ'. -/
@[simp]
-theorem weightedVsubVsubWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) :
- weightedVsubVsubWeights k i j j = -1 := by simp [weighted_vsub_vsub_weights, h.symm]
-#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVsubVsubWeights_apply_right
-
+theorem weightedVSubVSubWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) :
+ weightedVSubVSubWeights k i j j = -1 := by simp [weighted_vsub_vsub_weights, h.symm]
+#align finset.weighted_vsub_vsub_weights_apply_right Finset.weightedVSubVSubWeights_apply_right
+
+/- warning: finset.weighted_vsub_vsub_weights_apply_of_ne -> Finset.weightedVSubVSubWeights_apply_of_ne is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (Eq.{succ u1} k (Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVSubVSubWeights_apply_of_neₓ'. -/
@[simp]
-theorem weightedVsubVsubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i) (hj : t ≠ j) :
- weightedVsubVsubWeights k i j t = 0 := by simp [weighted_vsub_vsub_weights, hi, hj]
-#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVsubVsubWeights_apply_of_ne
-
+theorem weightedVSubVSubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i) (hj : t ≠ j) :
+ weightedVSubVSubWeights k i j t = 0 := by simp [weighted_vsub_vsub_weights, hi, hj]
+#align finset.weighted_vsub_vsub_weights_apply_of_ne Finset.weightedVSubVSubWeights_apply_of_ne
+
+/- warning: finset.sum_weighted_vsub_vsub_weights -> Finset.sum_weightedVSubVSubWeights is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u1}) [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.weightedVSubVSubWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j t)) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVSubVSubWeightsₓ'. -/
@[simp]
-theorem sum_weightedVsubVsubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
- (∑ t in s, weightedVsubVsubWeights k i j t) = 0 :=
+theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
+ (∑ t in s, weightedVSubVSubWeights k i j t) = 0 :=
by
simp_rw [weighted_vsub_vsub_weights, Pi.sub_apply, sum_sub_distrib]
simp [hi, hj]
-#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVsubVsubWeights
+#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVSubVSubWeights
variable {k}
+#print Finset.affineCombinationLineMapWeights /-
/-- Weights for expressing `line_map` as an affine combination. -/
def affineCombinationLineMapWeights [DecidableEq ι] (i j : ι) (c : k) : ι → k :=
- c • weightedVsubVsubWeights k j i + affineCombinationSingleWeights k i
+ c • weightedVSubVSubWeights k j i + affineCombinationSingleWeights k i
#align finset.affine_combination_line_map_weights Finset.affineCombinationLineMapWeights
+-/
+#print Finset.affineCombinationLineMapWeights_self /-
@[simp]
theorem affineCombinationLineMapWeights_self [DecidableEq ι] (i : ι) (c : k) :
affineCombinationLineMapWeights i i c = affineCombinationSingleWeights k i := by
simp [affine_combination_line_map_weights]
#align finset.affine_combination_line_map_weights_self Finset.affineCombinationLineMapWeights_self
+-/
+/- warning: finset.affine_combination_line_map_weights_apply_left -> Finset.affineCombinationLineMapWeights_apply_left is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (SubNegMonoid.toHasSub.{u1} k (AddGroup.toSubNegMonoid.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))) c))
+but is expected to have type
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Ne.{succ u2} ι i j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c i) (HSub.hSub.{u1, u1, u1} k k k (instHSub.{u1} k (Ring.toSub.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) c))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_line_map_weights_apply_left Finset.affineCombinationLineMapWeights_apply_leftₓ'. -/
@[simp]
theorem affineCombinationLineMapWeights_apply_left [DecidableEq ι] {i j : ι} (h : i ≠ j) (c : k) :
affineCombinationLineMapWeights i j c i = 1 - c := by
simp [affine_combination_line_map_weights, h.symm, sub_eq_neg_add]
#align finset.affine_combination_line_map_weights_apply_left Finset.affineCombinationLineMapWeights_apply_left
+#print Finset.affineCombinationLineMapWeights_apply_right /-
@[simp]
theorem affineCombinationLineMapWeights_apply_right [DecidableEq ι] {i j : ι} (h : i ≠ j) (c : k) :
affineCombinationLineMapWeights i j c j = c := by
simp [affine_combination_line_map_weights, h.symm]
#align finset.affine_combination_line_map_weights_apply_right Finset.affineCombinationLineMapWeights_apply_right
+-/
+/- warning: finset.affine_combination_line_map_weights_apply_of_ne -> Finset.affineCombinationLineMapWeights_apply_of_ne is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι} {t : ι}, (Ne.{succ u2} ι t i) -> (Ne.{succ u2} ι t j) -> (forall (c : k), Eq.{succ u1} k (Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (MonoidWithZero.toZero.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_line_map_weights_apply_of_ne Finset.affineCombinationLineMapWeights_apply_of_neₓ'. -/
@[simp]
theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi : t ≠ i)
(hj : t ≠ j) (c : k) : affineCombinationLineMapWeights i j c t = 0 := by
simp [affine_combination_line_map_weights, hi, hj]
#align finset.affine_combination_line_map_weights_apply_of_ne Finset.affineCombinationLineMapWeights_apply_of_ne
+/- warning: finset.sum_affine_combination_line_map_weights -> Finset.sum_affineCombinationLineMapWeights is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))))))
+but is expected to have type
+ forall {k : Type.{u1}} [_inst_1 : Ring.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_4 : DecidableEq.{succ u2} ι] {i : ι} {j : ι}, (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) j s) -> (forall (c : k), Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (t : ι) => Finset.affineCombinationLineMapWeights.{u1, u2} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c t)) (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_affine_combination_line_map_weights Finset.sum_affineCombinationLineMapWeightsₓ'. -/
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
(c : k) : (∑ t in s, affineCombinationLineMapWeights i j c t) = 1 :=
@@ -772,6 +1212,12 @@ include S
variable (k)
+/- warning: finset.affine_combination_affine_combination_single_weights -> Finset.affineCombination_affineCombinationSingleWeights is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationSingleWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i)) (p i))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeightsₓ'. -/
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p : ι → P) {i : ι}
@@ -782,18 +1228,30 @@ theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p :
simp [hj]
#align finset.affine_combination_affine_combination_single_weights Finset.affineCombination_affineCombinationSingleWeights
+/- warning: finset.weighted_vsub_weighted_vsub_vsub_weights -> Finset.weightedVSub_weightedVSubVSubWeights is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) S) (p i) (p j)))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [S : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.weightedVSubVSubWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) S) (p i) (p j)))
+Case conversion may be inaccurate. Consider using '#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeightsₓ'. -/
/-- A weighted subtraction with `weighted_vsub_vsub_weights` gives the result of subtracting the
specified points. -/
@[simp]
-theorem weightedVsub_weightedVsubVsubWeights [DecidableEq ι] (p : ι → P) {i j : ι} (hi : i ∈ s)
- (hj : j ∈ s) : s.weightedVsub p (weightedVsubVsubWeights k i j) = p i -ᵥ p j := by
+theorem weightedVSub_weightedVSubVSubWeights [DecidableEq ι] (p : ι → P) {i j : ι} (hi : i ∈ s)
+ (hj : j ∈ s) : s.weightedVSub p (weightedVSubVSubWeights k i j) = p i -ᵥ p j := by
rw [weighted_vsub_vsub_weights, ← affine_combination_vsub,
s.affine_combination_affine_combination_single_weights k p hi,
s.affine_combination_affine_combination_single_weights k p hj]
-#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVsub_weightedVsubVsubWeights
+#align finset.weighted_vsub_weighted_vsub_vsub_weights Finset.weightedVSub_weightedVSubVSubWeights
variable {k}
+/- warning: finset.affine_combination_affine_combination_line_map_weights -> Finset.affineCombination_affineCombinationLineMapWeights is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 S) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u1, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_4 : DecidableEq.{succ u4} ι] (p : ι -> P) {i : ι} {j : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (forall (c : k), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 S) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 S ι s p) (Finset.affineCombinationLineMapWeights.{u2, u4} k _inst_1 ι (fun (a : ι) (b : ι) => _inst_4 a b) i j c)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 S) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (p i) (p j)) c))
+Case conversion may be inaccurate. Consider using '#align finset.affine_combination_affine_combination_line_map_weights Finset.affineCombination_affineCombinationLineMapWeightsₓ'. -/
/-- An affine combination with `affine_combination_line_map_weights` gives the result of
`line_map`. -/
@[simp]
@@ -815,17 +1273,31 @@ variable (k : Type _) {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V
variable [affine_space V P] {ι : Type _} (s : Finset ι) {ι₂ : Type _} (s₂ : Finset ι₂)
+#print Finset.centroidWeights /-
/-- The weights for the centroid of some points. -/
def centroidWeights : ι → k :=
Function.const ι (card s : k)⁻¹
#align finset.centroid_weights Finset.centroidWeights
+-/
+/- warning: finset.centroid_weights_apply -> Finset.centroidWeights_apply is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) (i : ι), Eq.{succ u1} k (Finset.centroidWeights.{u1, u2} k _inst_1 ι s i) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) (i : ι), Eq.{succ u2} k (Finset.centroidWeights.{u2, u1} k _inst_1 ι s i) (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s)))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_apply Finset.centroidWeights_applyₓ'. -/
/-- `centroid_weights` at any point. -/
@[simp]
theorem centroidWeights_apply (i : ι) : s.centroidWeights k i = (card s : k)⁻¹ :=
rfl
#align finset.centroid_weights_apply Finset.centroidWeights_apply
+/- warning: finset.centroid_weights_eq_const -> Finset.centroidWeights_eq_const is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u1, u2} k _inst_1 ι s) (Function.const.{succ u1, succ u2} k ι (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s) (Function.const.{succ u2, succ u1} k ι (Inv.inv.{u2} k (DivisionRing.toInv.{u2} k _inst_1) (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s))))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_eq_const Finset.centroidWeights_eq_constₓ'. -/
/-- `centroid_weights` equals a constant function. -/
theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card s : k)⁻¹ :=
rfl
@@ -833,6 +1305,12 @@ theorem centroidWeights_eq_const : s.centroidWeights k = Function.const ι (card
variable {k}
+/- warning: finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero -> Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u2} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall {k : Type.{u2}} [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), (Ne.{succ u2} k (Nat.cast.{u2} k (NonAssocRing.toNatCast.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.card.{u1} ι s)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1))))))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zeroₓ'. -/
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0) :
@@ -841,12 +1319,24 @@ theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0)
variable (k)
+/- warning: finset.sum_centroid_weights_eq_one_of_card_ne_zero -> Finset.sum_centroidWeights_eq_one_of_card_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠ 0) :
(∑ i in s, s.centroidWeights k i) = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_card_ne_zero Finset.sum_centroidWeights_eq_one_of_card_ne_zero
+/- warning: finset.sum_centroid_weights_eq_one_of_nonempty -> Finset.sum_centroidWeights_eq_one_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
@@ -854,6 +1344,12 @@ theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
s.sum_centroidWeights_eq_one_of_card_ne_zero k (ne_of_gt (card_pos.2 h))
#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonempty
+/- warning: finset.sum_centroid_weights_eq_one_of_card_eq_add_one -> Finset.sum_centroidWeights_eq_one_of_card_eq_add_one is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) s (fun (i : ι) => Finset.centroidWeights.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h : card s = n + 1) :
@@ -863,18 +1359,32 @@ theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h
include V
+#print Finset.centroid /-
/-- The centroid of some points. Although defined for any `s`, this
is intended to be used in the case where the number of points,
converted to `k`, is not zero. -/
def centroid (p : ι → P) : P :=
s.affineCombination k p (s.centroidWeights k)
#align finset.centroid Finset.centroid
+-/
+/- warning: finset.centroid_def -> Finset.centroid_def is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u1, u4} k _inst_1 ι s))
+but is expected to have type
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (p : ι -> P), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u3 u1)) (succ u2)) (succ u4), succ (max u3 u1), succ u4} (AffineMap.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u1, max u3 u1, u2, u4} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u3} k _inst_1) (Pi.addCommGroup.{u1, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Pi.module.{u1, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k (DivisionRing.toRing.{u3} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u1} k (DivisionRing.toRing.{u3} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u4, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroidWeights.{u3, u1} k _inst_1 ι s))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_def Finset.centroid_defₓ'. -/
/-- The definition of the centroid. -/
theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
rfl
#align finset.centroid_def Finset.centroid_def
+/- warning: finset.centroid_univ -> Finset.centroid_univ is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Finset.{u3} P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) (Finset.Subtype.fintype.{u3} P s)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} P) Type.{u3} (Finset.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Finset.{u3} P) (Finset.hasMem.{u3} P) x s))))))) (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 P s (id.{succ u3} P))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Finset.{u3} P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.univ.{u3} (Subtype.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s)) (Finset.Subtype.fintype.{u3} P s)) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Finset.{u3} P) (Finset.instMembershipFinset.{u3} P) x s))) (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 P s (id.{succ u3} P))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_univ Finset.centroid_univₓ'. -/
theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centroid k id :=
by
rw [centroid, centroid, ← s.attach_affine_combination_coe]
@@ -883,12 +1393,24 @@ theorem centroid_univ (s : Finset P) : univ.centroid k (coe : s → P) = s.centr
simp
#align finset.centroid_univ Finset.centroid_univ
+/- warning: finset.centroid_singleton -> Finset.centroid_singleton is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P) (i : ι), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.hasSingleton.{u4} ι) i) p) (p i)
+but is expected to have type
+ forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u1}} (p : ι -> P) (i : ι), Eq.{succ u4} P (Finset.centroid.{u3, u2, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Singleton.singleton.{u1, u1} ι (Finset.{u1} ι) (Finset.instSingletonFinset.{u1} ι) i) p) (p i)
+Case conversion may be inaccurate. Consider using '#align finset.centroid_singleton Finset.centroid_singletonₓ'. -/
/-- The centroid of a single point. -/
@[simp]
theorem centroid_singleton (p : ι → P) (i : ι) : ({i} : Finset ι).centroid k p = p i := by
simp [centroid_def, affine_combination_apply]
#align finset.centroid_singleton Finset.centroid_singleton
+/- warning: finset.centroid_pair -> Finset.centroid_pair is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.hasInsert.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.hasSingleton.{u4} ι) i₂)) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
+but is expected to have type
+ forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : DecidableEq.{succ u4} ι] [_inst_6 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : ι -> P) (i₁ : ι) (i₂ : ι), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Insert.insert.{u4, u4} ι (Finset.{u4} ι) (Finset.instInsertFinset.{u4} ι (fun (a : ι) (b : ι) => _inst_5 a b)) i₁ (Singleton.singleton.{u4, u4} ι (Finset.{u4} ι) (Finset.instSingletonFinset.{u4} ι) i₂)) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p i₂) (p i₁))) (p i₁))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_pair Finset.centroid_pairₓ'. -/
/-- The centroid of two points, expressed directly as adding a vector
to a point. -/
theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁ i₂ : ι) :
@@ -907,6 +1429,12 @@ theorem centroid_pair [DecidableEq ι] [Invertible (2 : k)] (p : ι → P) (i₁
simp [h]
#align finset.centroid_pair Finset.centroid_pair
+/- warning: finset.centroid_pair_fin -> Finset.centroid_pair_fin is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) p) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k _inst_1)) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k _inst_1))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))) (p (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
+but is expected to have type
+ forall (k : Type.{u3}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Invertible.{u3} k (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1)))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (p : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> P), Eq.{succ u2} P (Finset.centroid.{u3, u1, u2, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Finset.univ.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) p) (HVAdd.hVAdd.{u1, u2, u2} V P P (instHVAdd.{u1, u2} V P (AddAction.toVAdd.{u1, u2} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u3, u1, u1} k V V (instHSMul.{u3, u1} k V (SMulZeroClass.toSMul.{u3, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u1} k V (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u1} k V (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Inv.inv.{u3} k (DivisionRing.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_pair_fin Finset.centroid_pair_finₓ'. -/
/-- The centroid of two points indexed by `fin 2`, expressed directly
as adding a vector to the first point. -/
theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
@@ -916,6 +1444,12 @@ theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
convert centroid_pair k p 0 1
#align finset.centroid_pair_fin Finset.centroid_pair_fin
+/- warning: finset.centroid_map -> Finset.centroid_map is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) (Finset.centroid.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (coeFn.{max 1 (succ u5) (succ u4), max (succ u5) (succ u4)} (Function.Embedding.{succ u5, succ u4} ι₂ ι) (fun (_x : Function.Embedding.{succ u5, succ u4} ι₂ ι) => ι₂ -> ι) (Function.Embedding.hasCoeToFun.{succ u5, succ u4} ι₂ ι) e)))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) (e : Function.Embedding.{succ u5, succ u4} ι₂ ι) (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.map.{u5, u4} ι₂ ι e s₂) p) (Finset.centroid.{u2, u1, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ (Function.comp.{succ u5, succ u4, succ u3} ι₂ ι P p (FunLike.coe.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : ι₂) => ι) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u5), succ u5, succ u4} (Function.Embedding.{succ u5, succ u4} ι₂ ι) ι₂ ι (Function.instEmbeddingLikeEmbedding.{succ u5, succ u4} ι₂ ι)) e)))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_map Finset.centroid_mapₓ'. -/
/-- A centroid, over the image of an embedding, equals a centroid with
the same points and weights over the original `finset`. -/
theorem centroid_map (e : ι₂ ↪ ι) (p : ι → P) : (s₂.map e).centroid k p = s₂.centroid k (p ∘ e) :=
@@ -924,6 +1458,7 @@ theorem centroid_map (e : ι₂ ↪ ι) (p : ι → P) : (s₂.map e).centroid k
omit V
+#print Finset.centroidWeightsIndicator /-
/-- `centroid_weights` gives the weights for the centroid as a
constant function, which is suitable when summing over the points
whose centroid is being taken. This function gives the weights in a
@@ -933,19 +1468,34 @@ In the case of a `fintype`, the sum may be over `univ`. -/
def centroidWeightsIndicator : ι → k :=
Set.indicator (↑s) (s.centroidWeights k)
#align finset.centroid_weights_indicator Finset.centroidWeightsIndicator
+-/
+/- warning: finset.centroid_weights_indicator_def -> Finset.centroidWeightsIndicator_def is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s) (Set.indicator.{u2, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s) (Finset.centroidWeights.{u1, u2} k _inst_1 ι s))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι), Eq.{max (succ u2) (succ u1)} (ι -> k) (Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s) (Set.indicator.{u1, u2} ι k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)))) (Finset.toSet.{u1} ι s) (Finset.centroidWeights.{u2, u1} k _inst_1 ι s))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_weights_indicator_def Finset.centroidWeightsIndicator_defₓ'. -/
/-- The definition of `centroid_weights_indicator`. -/
theorem centroidWeightsIndicator_def :
s.centroidWeightsIndicator k = Set.indicator (↑s) (s.centroidWeights k) :=
rfl
#align finset.centroid_weights_indicator_def Finset.centroidWeightsIndicator_def
+#print Finset.sum_centroidWeightsIndicator /-
/-- The sum of the weights for the centroid indexed by a `fintype`. -/
theorem sum_centroidWeightsIndicator [Fintype ι] :
(∑ i, s.centroidWeightsIndicator k i) = ∑ i in s, s.centroidWeights k i :=
(Set.sum_indicator_subset _ (subset_univ _)).symm
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
+-/
+/- warning: finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero -> Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Ne.{1} Nat (Finset.card.{u2} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Ne.{1} Nat (Finset.card.{u1} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is not
zero. -/
@@ -956,6 +1506,12 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
exact s.sum_centroid_weights_eq_one_of_card_ne_zero k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero
+/- warning: finset.sum_centroid_weights_indicator_eq_one_of_nonempty -> Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι], (Finset.Nonempty.{u2} ι s) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι], (Finset.Nonempty.{u1} ι s) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the set is nonempty. -/
theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι] (h : s.Nonempty) :
@@ -965,6 +1521,12 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
exact s.sum_centroid_weights_eq_one_of_nonempty k h
#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty
+/- warning: finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one -> Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) [_inst_1 : DivisionRing.{u1} k] {ι : Type.{u2}} (s : Finset.{u2} ι) [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] [_inst_6 : Fintype.{u2} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u2} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u2} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u1, u2} k _inst_1 ι s i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))
+but is expected to have type
+ forall (k : Type.{u2}) [_inst_1 : DivisionRing.{u2} k] {ι : Type.{u1}} (s : Finset.{u1} ι) [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_1)))] [_inst_6 : Fintype.{u1} ι] {n : Nat}, (Eq.{1} Nat (Finset.card.{u1} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (Finset.univ.{u1} ι _inst_6) (fun (i : ι) => Finset.centroidWeightsIndicator.{u2, u1} k _inst_1 ι s i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the weights in the centroid
indexed by a `fintype` sum to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fintype ι] {n : ℕ}
@@ -976,12 +1538,24 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fin
include V
+/- warning: finset.centroid_eq_affine_combination_fintype -> Finset.centroid_eq_affineCombination_fintype is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u1} k _inst_1) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u1, u4} k _inst_1 ι s))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P (DivisionRing.toRing.{u2} k _inst_1) (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k (DivisionRing.toRing.{u2} k _inst_1) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P (DivisionRing.toRing.{u2} k _inst_1) _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) (Finset.centroidWeightsIndicator.{u2, u4} k _inst_1 ι s))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintypeₓ'. -/
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
s.centroid k p = univ.affineCombination k p (s.centroidWeightsIndicator k) :=
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
+/- warning: finset.centroid_eq_centroid_image_of_inj_on -> Finset.centroid_eq_centroid_image_of_inj_on is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {p : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (forall (j : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {ps : Set.{u3} P} [_inst_5 : Fintype.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps)], (Eq.{succ u3} (Set.{u3} P) ps (Set.image.{u4, u3} ι P p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s))) -> (Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) (Finset.univ.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) _inst_5) (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) ps) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x ps))))) x))))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {p : ι -> P}, (forall (i : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall (j : ι), (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {ps : Set.{u3} P} [_inst_5 : Fintype.{u3} (Set.Elem.{u3} P ps)], (Eq.{succ u3} (Set.{u3} P) ps (Set.image.{u4, u3} ι P p (Finset.toSet.{u4} ι s))) -> (Eq.{succ u3} P (Finset.centroid.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u2, u1, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.Elem.{u3} P ps) (Finset.univ.{u3} (Set.Elem.{u3} P ps) _inst_5) (fun (x : Set.Elem.{u3} P ps) => Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) x ps) x))))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_onₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
@@ -1017,6 +1591,12 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
rw [(hf' x).2]
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
+/- warning: finset.centroid_eq_of_inj_on_of_image_eq -> Finset.centroid_eq_of_inj_on_of_image_eq is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : Finset.{u4} ι) {ι₂ : Type.{u5}} (s₂ : Finset.{u5} ι₂) {p : ι -> P}, (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (forall (j : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u3} P (p i) (p j)) -> (Eq.{succ u4} ι i j))) -> (forall {p₂ : ι₂ -> P}, (forall (i : ι₂), (Membership.Mem.{u5, u5} ι₂ (Finset.{u5} ι₂) (Finset.hasMem.{u5} ι₂) i s₂) -> (forall (j : ι₂), (Membership.Mem.{u5, u5} ι₂ (Finset.{u5} ι₂) (Finset.hasMem.{u5} ι₂) j s₂) -> (Eq.{succ u3} P (p₂ i) (p₂ j)) -> (Eq.{succ u5} ι₂ i j))) -> (Eq.{succ u3} (Set.{u3} P) (Set.image.{u4, u3} ι P p ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s)) (Set.image.{u5, u3} ι₂ P p₂ ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (Finset.{u5} ι₂) (Set.{u5} ι₂) (HasLiftT.mk.{succ u5, succ u5} (Finset.{u5} ι₂) (Set.{u5} ι₂) (CoeTCₓ.coe.{succ u5, succ u5} (Finset.{u5} ι₂) (Set.{u5} ι₂) (Finset.Set.hasCoeT.{u5} ι₂))) s₂))) -> (Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ p₂)))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u4}} [_inst_1 : DivisionRing.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u4} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u5}} (s : Finset.{u5} ι) {ι₂ : Type.{u3}} (s₂ : Finset.{u3} ι₂) {p : ι -> P}, (forall (i : ι), (Membership.mem.{u5, u5} ι (Finset.{u5} ι) (Finset.instMembershipFinset.{u5} ι) i s) -> (forall (j : ι), (Membership.mem.{u5, u5} ι (Finset.{u5} ι) (Finset.instMembershipFinset.{u5} ι) j s) -> (Eq.{succ u4} P (p i) (p j)) -> (Eq.{succ u5} ι i j))) -> (forall {p₂ : ι₂ -> P}, (forall (i : ι₂), (Membership.mem.{u3, u3} ι₂ (Finset.{u3} ι₂) (Finset.instMembershipFinset.{u3} ι₂) i s₂) -> (forall (j : ι₂), (Membership.mem.{u3, u3} ι₂ (Finset.{u3} ι₂) (Finset.instMembershipFinset.{u3} ι₂) j s₂) -> (Eq.{succ u4} P (p₂ i) (p₂ j)) -> (Eq.{succ u3} ι₂ i j))) -> (Eq.{succ u4} (Set.{u4} P) (Set.image.{u5, u4} ι P p (Finset.toSet.{u5} ι s)) (Set.image.{u3, u4} ι₂ P p₂ (Finset.toSet.{u3} ι₂ s₂))) -> (Eq.{succ u4} P (Finset.centroid.{u2, u1, u4, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (Finset.centroid.{u2, u1, u4, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι₂ s₂ p₂)))
+Case conversion may be inaccurate. Consider using '#align finset.centroid_eq_of_inj_on_of_image_eq Finset.centroid_eq_of_inj_on_of_image_eqₓ'. -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
/-- Two indexed families of points that are injective on the given
@@ -1041,18 +1621,24 @@ variable {ι : Type _}
include V
+/- warning: weighted_vsub_mem_vector_span -> weightedVSub_mem_vectorSpan is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (forall (p : ι -> P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p)))
+Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpanₓ'. -/
/-- A `weighted_vsub` with sum of weights 0 is in the `vector_span` of
an indexed family. -/
-theorem weightedVsub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
- (p : ι → P) : s.weightedVsub p w ∈ vectorSpan k (Set.range p) := by
+theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
+ (p : ι → P) : s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
classical
rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
· skip
simp [Finset.eq_empty_of_isEmpty s]
· rw [vectorSpan_range_eq_span_range_vsub_right k p i0, ← Set.image_univ,
Finsupp.mem_span_image_iff_total,
- Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero s w p h (p i0),
- Finset.weightedVsubOfPoint_apply]
+ Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p h (p i0),
+ Finset.weightedVSubOfPoint_apply]
let w' := Set.indicator (↑s) w
have hwx : ∀ i, w' i ≠ 0 → i ∈ s := fun i => Set.mem_of_indicator_ne_zero
use Finsupp.onFinset s w' hwx, Set.subset_univ _
@@ -1061,8 +1647,14 @@ theorem weightedVsub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
intro i hi
simp [w', Set.indicator_apply, if_pos hi]
· exact fun _ => zero_smul k _
-#align weighted_vsub_mem_vector_span weightedVsub_mem_vectorSpan
-
+#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
+
+/- warning: affine_combination_mem_affine_span -> affineCombination_mem_affineSpan is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (forall (p : ι -> P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {s : Finset.{u4} ι} {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (forall (p : ι -> P), Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span affineCombination_mem_affineSpanₓ'. -/
/-- An `affine_combination` with sum of weights 1 is in the
`affine_span` of an indexed family, if the underlying ring is
nontrivial. -/
@@ -1082,7 +1674,7 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
by
rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
- apply weightedVsub_mem_vectorSpan
+ apply weightedVSub_mem_vectorSpan
simp [Pi.sub_apply, h, hw1]
rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
@@ -1090,11 +1682,17 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
variable (k) {V}
+/- warning: mem_vector_span_iff_eq_weighted_vsub -> mem_vectorSpan_iff_eq_weightedVSub is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) (fun (h : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) => Eq.{succ u2} V v (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+but is expected to have type
+ forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} {v : V} {p : ι -> P}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u1, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) (fun (h : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)))))) => Eq.{succ u3} V v (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), max (succ u4) (succ u2), succ u3} (LinearMap.{u2, u2, max u2 u4, u3} k k (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u4 u2, u3} k k (ι -> k) V (Ring.toSemiring.{u2} k _inst_1) (Ring.toSemiring.{u2} k _inst_1) (Pi.addCommMonoid.{u4, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) _inst_3 (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.weightedVSub.{u2, u3, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+Case conversion may be inaccurate. Consider using '#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSubₓ'. -/
/-- A vector is in the `vector_span` of an indexed family if and only
if it is a `weighted_vsub` with sum of weights 0. -/
-theorem mem_vectorSpan_iff_eq_weightedVsub {v : V} {p : ι → P} :
+theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k)(h : (∑ i in s, w i) = 0), v = s.weightedVsub p w :=
+ ∃ (s : Finset ι)(w : ι → k)(h : (∑ i in s, w i) = 0), v = s.weightedVSub p w :=
by
classical
constructor
@@ -1118,8 +1716,8 @@ theorem mem_vectorSpan_iff_eq_weightedVsub {v : V} {p : ι → P} :
use hw
have hz : w i0 • (p i0 -ᵥ p i0 : V) = 0 := (vsub_self (p i0)).symm ▸ smul_zero _
change (fun i => w i • (p i -ᵥ p i0 : V)) i0 = 0 at hz
- rw [Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero _ w p hw (p i0),
- Finset.weightedVsubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
+ rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w p hw (p i0),
+ Finset.weightedVSubOfPoint_apply, ← hv, Finsupp.total_apply, Finset.sum_insert_zero hz]
change (∑ i in l.support, l i • _) = _
congr with i
by_cases h : i = i0
@@ -1131,11 +1729,17 @@ theorem mem_vectorSpan_iff_eq_weightedVsub {v : V} {p : ι → P} :
use ∅
simp
· rintro ⟨s, w, hw, rfl⟩
- exact weightedVsub_mem_vectorSpan hw p
-#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVsub
+ exact weightedVSub_mem_vectorSpan hw p
+#align mem_vector_span_iff_eq_weighted_vsub mem_vectorSpan_iff_eq_weightedVSub
variable {k}
+/- warning: eq_affine_combination_of_mem_affine_span -> eq_affineCombination_of_mem_affineSpan is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpanₓ'. -/
/-- A point in the `affine_span` of an indexed family is an
`affine_combination` with sum of weights 1. See also
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
@@ -1149,7 +1753,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
have h0 : p i0 ∈ affineSpan k (Set.range p) := mem_affineSpan k (Set.mem_range_self i0)
have hd : p1 -ᵥ p i0 ∈ (affineSpan k (Set.range p)).direction :=
AffineSubspace.vsub_mem_direction h h0
- rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVsub] at hd
+ rw [direction_affineSpan, mem_vectorSpan_iff_eq_weightedVSub] at hd
rcases hd with ⟨s, w, h, hs⟩
let s' := insert i0 s
let w' := Set.indicator (↑s) w
@@ -1158,7 +1762,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
have hs' : s'.weighted_vsub p w' = p1 -ᵥ p i0 :=
by
rw [hs]
- exact (Finset.weightedVsub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
+ exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
let w0 : ι → k := Function.update (Function.const ι 0) i0 1
have hw0 : (∑ i in s', w0 i) = 1 := by
rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
@@ -1168,9 +1772,15 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
use s', w0 + w'
constructor
· simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']
- · rw [add_comm, ← Finset.weightedVsub_vadd_affineCombination, hw0s, hs', vsub_vadd]
+ · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
+/- warning: eq_affine_combination_of_mem_affine_span_of_fintype -> eq_affineCombination_of_mem_affineSpan_of_fintype is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+but is expected to have type
+ forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] {p1 : P} {p : ι -> P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) -> (Exists.{max (succ u2) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) (fun (hw : Eq.{succ u2} k (Finset.sum.{u2, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1))))) => Eq.{succ u3} P p1 (FunLike.coe.{max (max (succ (max u2 u4)) (succ u1)) (succ u3), succ (max u2 u4), succ u3} (AffineMap.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u2, max u2 u4, max u2 u4, u1, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_1)) (Pi.module.{u4, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u2, u1, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w))))
+Case conversion may be inaccurate. Consider using '#align eq_affine_combination_of_mem_affine_span_of_fintype eq_affineCombination_of_mem_affineSpan_of_fintypeₓ'. -/
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
∃ (w : ι → k)(hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
@@ -1184,6 +1794,12 @@ theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P}
variable (k V)
+/- warning: mem_affine_span_iff_eq_affine_combination -> mem_affineSpan_iff_eq_affineCombination is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p1 : P} {p : ι -> P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) (fun (hw : Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) => Eq.{succ u3} P p1 (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+but is expected to have type
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] {p1 : P} {p : ι -> P}, Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Exists.{0} (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (fun (hw : Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) => Eq.{succ u2} P p1 (FunLike.coe.{max (max (succ (max u3 u4)) (succ u1)) (succ u2), succ (max u3 u4), succ u2} (AffineMap.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u1, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w)))))
+Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombinationₓ'. -/
/-- A point is in the `affine_span` of an indexed family if and only
if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
@@ -1197,12 +1813,18 @@ theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι
exact affineCombination_mem_affineSpan hw p
#align mem_affine_span_iff_eq_affine_combination mem_affineSpan_iff_eq_affineCombination
+/- warning: mem_affine_span_iff_eq_weighted_vsub_of_point_vadd -> mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u4) (succ u1)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u3} P q (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSubOfPoint.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+but is expected to have type
+ forall (k : Type.{u3}) (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u3} k] (p : ι -> P) (j : ι) (q : P), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) q (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p))) (Exists.{succ u4} (Finset.{u4} ι) (fun (s : Finset.{u4} ι) => Exists.{max (succ u3) (succ u4)} (ι -> k) (fun (w : ι -> k) => Eq.{succ u2} P q (HVAdd.hVAdd.{u1, u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P P (instHVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddAction.toVAdd.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (SubNegMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2))) (AddTorsor.toAddAction.{u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) P (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) _inst_2) _inst_4))) (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u1} (LinearMap.{u3, u3, max u3 u4, u1} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u1} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.219 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSubOfPoint.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p (p j)) w) (p j)))))
+Case conversion may be inaccurate. Consider using '#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddₓ'. -/
/-- Given a family of points together with a chosen base point in that family, membership of the
affine span of this family corresponds to an identity in terms of `weighted_vsub_of_point`, with
weights that are not required to sum to 1. -/
-theorem mem_affineSpan_iff_eq_weightedVsubOfPoint_vadd [Nontrivial k] (p : ι → P) (j : ι) (q : P) :
+theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι → P) (j : ι) (q : P) :
q ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k), q = s.weightedVsubOfPoint p (p j) w +ᵥ p j :=
+ ∃ (s : Finset ι)(w : ι → k), q = s.weightedVSubOfPoint p (p j) w +ᵥ p j :=
by
constructor
· intro hq
@@ -1220,12 +1842,18 @@ theorem mem_affineSpan_iff_eq_weightedVsubOfPoint_vadd [Nontrivial k] (p : ι
simp [w', hij]
rw [s.weighted_vsub_of_point_eq_of_weights_eq p j w w' hww, ←
s.weighted_vsub_of_point_insert w' p j, ←
- (insert j s).affineCombination_eq_weightedVsubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
+ (insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
exact affineCombination_mem_affineSpan h₁ p
-#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVsubOfPoint_vadd
+#align mem_affine_span_iff_eq_weighted_vsub_of_point_vadd mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd
variable {k V}
+/- warning: affine_span_eq_affine_span_line_map_units -> affineSpan_eq_affineSpan_lineMap_units is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] [_inst_5 : Nontrivial.{u1} k] {s : Set.{u3} P} {p : P}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p s) -> (forall (w : (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) -> (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1))), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u3} P (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) (fun (q : coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) => coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x s))))) q)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (coeBase.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (Units.hasCoe.{u1} k (Ring.toMonoid.{u1} k _inst_1))))) (w q))))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] [_inst_5 : Nontrivial.{u3} k] {s : Set.{u2} P} {p : P}, (Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) p s) -> (forall (w : (Set.Elem.{u2} P s) -> (Units.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))))), Eq.{succ u2} (AffineSubspace.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u2} P (Set.Elem.{u2} P s) (fun (q : Set.Elem.{u2} P s) => FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u1, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 p (Subtype.val.{succ u2} P (fun (x : P) => Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) x s) q)) (Units.val.{u3} k (MonoidWithZero.toMonoid.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (w q))))) (affineSpan.{u3, u1, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_unitsₓ'. -/
/-- Given a set of points, together with a chosen base point in this set, if we affinely transport
all other members of the set along the line joining them to this base point, the affine span is
unchanged. -/
@@ -1236,7 +1864,7 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
have : s = Set.range (coe : s → P) := by simp
conv_rhs => rw [this]
apply le_antisymm <;> intro q hq <;>
- erw [mem_affineSpan_iff_eq_weightedVsubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq⊢ <;>
+ erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq⊢ <;>
obtain ⟨t, μ, rfl⟩ := hq <;>
use t <;>
[use fun x => μ x * ↑(w x), use fun x => μ x * ↑(w x)⁻¹] <;>
@@ -1255,6 +1883,12 @@ include V
open Set Finset
+/- warning: centroid_mem_affine_span_of_cast_card_ne_zero -> centroid_mem_affineSpan_of_cast_card_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u1} k ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u1} Nat k (CoeTCₓ.coe.{1, succ u1} Nat k (Nat.castCoe.{u1} k (AddMonoidWithOne.toNatCast.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u3, u1} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} {s : Finset.{u4} ι} (p : ι -> P), (Ne.{succ u3} k (Nat.cast.{u3} k (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k _inst_1))) (Finset.card.{u4} ι s)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1))))))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u3, u1, u2, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u3, u1, u2} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u4} P ι p)))
+Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_cast_card_ne_zero centroid_mem_affineSpan_of_cast_card_ne_zeroₓ'. -/
/-- The centroid lies in the affine span if the number of points,
converted to `k`, is not zero. -/
theorem centroid_mem_affineSpan_of_cast_card_ne_zero {s : Finset ι} (p : ι → P)
@@ -1264,6 +1898,12 @@ theorem centroid_mem_affineSpan_of_cast_card_ne_zero {s : Finset ι} (p : ι →
variable (k)
+/- warning: centroid_mem_affine_span_of_card_ne_zero -> centroid_mem_affineSpan_of_card_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P), (Ne.{1} Nat (Finset.card.{u4} ι s) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P), (Ne.{1} Nat (Finset.card.{u3} ι s) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
+Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_card_ne_zero centroid_mem_affineSpan_of_card_ne_zeroₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is not zero. -/
theorem centroid_mem_affineSpan_of_card_ne_zero [CharZero k] {s : Finset ι} (p : ι → P)
@@ -1271,6 +1911,12 @@ theorem centroid_mem_affineSpan_of_card_ne_zero [CharZero k] {s : Finset ι} (p
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_card_ne_zero k h) p
#align centroid_mem_affine_span_of_card_ne_zero centroid_mem_affineSpan_of_card_ne_zero
+/- warning: centroid_mem_affine_span_of_nonempty -> centroid_mem_affineSpan_of_nonempty is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P), (Finset.Nonempty.{u4} ι s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P), (Finset.Nonempty.{u3} ι s) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
+Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_nonempty centroid_mem_affineSpan_of_nonemptyₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the set is nonempty. -/
theorem centroid_mem_affineSpan_of_nonempty [CharZero k] {s : Finset ι} (p : ι → P)
@@ -1278,6 +1924,12 @@ theorem centroid_mem_affineSpan_of_nonempty [CharZero k] {s : Finset ι} (p : ι
affineCombination_mem_affineSpan (s.sum_centroidWeights_eq_one_of_nonempty k h) p
#align centroid_mem_affine_span_of_nonempty centroid_mem_affineSpan_of_nonempty
+/- warning: centroid_mem_affine_span_of_card_eq_add_one -> centroid_mem_affineSpan_of_card_eq_add_one is a dubious translation:
+lean 3 declaration is
+ forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k _inst_1))))] {s : Finset.{u4} ι} (p : ι -> P) {n : Nat}, (Eq.{1} Nat (Finset.card.{u4} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u3, succ u4} P ι p)))
+but is expected to have type
+ forall (k : Type.{u4}) {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : DivisionRing.{u4} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u4, u1} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u3}} [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_1)))] {s : Finset.{u3} ι} (p : ι -> P) {n : Nat}, (Eq.{1} Nat (Finset.card.{u3} ι s) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4)) (Finset.centroid.{u4, u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) (affineSpan.{u4, u1, u2} k V P (DivisionRing.toRing.{u4} k _inst_1) _inst_2 _inst_3 _inst_4 (Set.range.{u2, succ u3} P ι p)))
+Case conversion may be inaccurate. Consider using '#align centroid_mem_affine_span_of_card_eq_add_one centroid_mem_affineSpan_of_card_eq_add_oneₓ'. -/
/-- In the characteristic zero case, the centroid lies in the affine
span if the number of points is `n + 1`. -/
theorem centroid_mem_affineSpan_of_card_eq_add_one [CharZero k] {s : Finset ι} (p : ι → P) {n : ℕ}
@@ -1295,17 +1947,23 @@ variable [affine_space V P] {ι : Type _} (s : Finset ι)
include V
+/- warning: affine_map.weighted_vsub_of_point -> AffineMap.weightedVSubOfPoint is a dubious translation:
+lean 3 declaration is
+ forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u4 u2, max u4 u3, u2, u2} k (Prod.{max u4 u2, u2} (ι -> V) V) (Prod.{max u4 u3, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.addCommGroup.{max u4 u2, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u4 u2, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u2} ι k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _inst_3) (Prod.addTorsor.{max u4 u2, max u4 u3, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (Pi.addTorsor.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2) (fun (ᾰ : ι) => P) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
+but is expected to have type
+ forall {k : Type.{u1}} {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : CommRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}}, (Finset.{u4} ι) -> (ι -> k) -> (AffineMap.{u1, max u2 u4, max u3 u4, u2, u2} k (Prod.{max u2 u4, u2} (ι -> V) V) (Prod.{max u3 u4, u3} (ι -> P) P) V V (CommRing.toRing.{u1} k _inst_1) (Prod.instAddCommGroupSum.{max u2 u4, u2} (ι -> V) V (Pi.addCommGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => _inst_2)) _inst_2) (Prod.module.{u1, max u2 u4, u2} k (ι -> V) V (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (Pi.addCommMonoid.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u2, u1} ι (fun (i : ι) => V) k (Ring.toSemiring.{u1} k (CommRing.toRing.{u1} k _inst_1)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (fun (i : ι) => _inst_3)) _inst_3) (Prod.instAddTorsorProdProdInstAddGroupSum.{max u2 u4, max u3 u4, u2, u3} (ι -> V) (ι -> P) V P (Pi.addGroup.{u4, u2} ι (fun (i : ι) => V) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} V _inst_2)) (AddCommGroup.toAddGroup.{u2} V _inst_2) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u4, u2, u3} ι (fun (i : ι) => V) (fun (i : ι) => P) (fun (ᾰ : ι) => _inst_2) (fun (i : ι) => _inst_4)) _inst_4) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))
+Case conversion may be inaccurate. Consider using '#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPointₓ'. -/
-- TODO: define `affine_map.proj`, `affine_map.fst`, `affine_map.snd`
/-- A weighted sum, as an affine map on the points involved. -/
-def weightedVsubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
+def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
where
- toFun p := s.weightedVsubOfPoint p.fst p.snd w
+ toFun p := s.weightedVSubOfPoint p.fst p.snd w
linear := ∑ i in s, w i • ((LinearMap.proj i).comp (LinearMap.fst _ _ _) - LinearMap.snd _ _ _)
map_vadd' := by
rintro ⟨p, b⟩ ⟨v, b'⟩
- simp [LinearMap.sum_apply, Finset.weightedVsubOfPoint, vsub_vadd_eq_vsub_sub, vadd_vsub_assoc,
+ simp [LinearMap.sum_apply, Finset.weightedVSubOfPoint, vsub_vadd_eq_vsub_sub, vadd_vsub_assoc,
add_sub, ← sub_add_eq_add_sub, smul_add, Finset.sum_add_distrib]
-#align affine_map.weighted_vsub_of_point AffineMap.weightedVsubOfPoint
+#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPoint
end AffineMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 87c54600fe3cdc7d32ff5b50873ac724d86aef8d
+! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -376,6 +376,8 @@ theorem weightedVsub_const_smul (w : ι → k) (p : ι → P) (c : k) :
s.weightedVsubOfPoint_const_smul _ _ _ _
#align finset.weighted_vsub_const_smul Finset.weightedVsub_const_smul
+variable (k)
+
/-- A weighted sum of the results of subtracting a default base point
from the given points, added to that base point, as an affine map on
the weights. This is intended to be used when the sum of the weights
@@ -393,10 +395,12 @@ def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
`weighted_vsub`. -/
@[simp]
theorem affineCombination_linear (p : ι → P) :
- (s.affineCombination p : (ι → k) →ᵃ[k] P).linear = s.weightedVsub p :=
+ (s.affineCombination k p).linear = s.weightedVsub p :=
rfl
#align finset.affine_combination_linear Finset.affineCombination_linear
+variable {k}
+
/-- Applying `affine_combination` with given weights. This is for the
case where a result involving a default base point is OK (for example,
when that base point will cancel out later); a more typical use case
@@ -405,7 +409,7 @@ point with
`affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one` and
then using `weighted_vsub_of_point_apply`. -/
theorem affineCombination_apply (w : ι → k) (p : ι → P) :
- s.affineCombination p w =
+ s.affineCombination k p w =
s.weightedVsubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty :=
rfl
#align finset.affine_combination_apply Finset.affineCombination_apply
@@ -413,14 +417,14 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
/-- The value of `affine_combination`, where the given points are equal. -/
@[simp]
theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 1) :
- s.affineCombination (fun _ => p) w = p := by
+ s.affineCombination k (fun _ => p) w = p := by
rw [affine_combination_apply, s.weighted_vsub_of_point_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
/-- `affine_combination` gives equal results for two families of weights and two families of
points that are equal on `s`. -/
theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i = w₂ i) {p₁ p₂ : ι → P}
- (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.affineCombination p₁ w₁ = s.affineCombination p₂ w₂ := by
+ (hp : ∀ i ∈ s, p₁ i = p₂ i) : s.affineCombination k p₁ w₁ = s.affineCombination k p₂ w₂ := by
simp_rw [affine_combination_apply, s.weighted_vsub_of_point_congr hw hp]
#align finset.affine_combination_congr Finset.affineCombination_congr
@@ -428,25 +432,25 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
sum of the weights is 1. -/
theorem affineCombination_eq_weightedVsubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
(h : (∑ i in s, w i) = 1) (b : P) :
- s.affineCombination p w = s.weightedVsubOfPoint p b w +ᵥ b :=
+ s.affineCombination k p w = s.weightedVsubOfPoint p b w +ᵥ b :=
s.weightedVsubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVsubOfPoint_vadd_of_sum_eq_one
/-- Adding a `weighted_vsub` to an `affine_combination`. -/
theorem weightedVsub_vadd_affineCombination (w₁ w₂ : ι → k) (p : ι → P) :
- s.weightedVsub p w₁ +ᵥ s.affineCombination p w₂ = s.affineCombination p (w₁ + w₂) := by
+ s.weightedVsub p w₁ +ᵥ s.affineCombination k p w₂ = s.affineCombination k p (w₁ + w₂) := by
rw [← vadd_eq_add, AffineMap.map_vadd, affine_combination_linear]
#align finset.weighted_vsub_vadd_affine_combination Finset.weightedVsub_vadd_affineCombination
/-- Subtracting two `affine_combination`s. -/
theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
- s.affineCombination p w₁ -ᵥ s.affineCombination p w₂ = s.weightedVsub p (w₁ - w₂) := by
+ s.affineCombination k p w₁ -ᵥ s.affineCombination k p w₂ = s.weightedVsub p (w₁ - w₂) := by
rw [← AffineMap.linearMap_vsub, affine_combination_linear, vsub_eq_sub]
#align finset.affine_combination_vsub Finset.affineCombination_vsub
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
- s.attach.affineCombination f (w ∘ f) = (image f univ).affineCombination id w :=
+ s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w :=
by
simp only [affine_combination, weighted_vsub_of_point_apply, id.def, vadd_right_cancel_iff,
Function.comp_apply, AffineMap.coe_mk]
@@ -461,7 +465,7 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
- s.attach.affineCombination (coe : s → P) (w ∘ coe) = s.affineCombination id w := by
+ s.attach.affineCombination k (coe : s → P) (w ∘ coe) = s.affineCombination k id w := by
classical rw [attach_affine_combination_of_injective s w (coe : s → P) Subtype.coe_injective,
univ_eq_attach, attach_image_coe]
#align finset.attach_affine_combination_coe Finset.attach_affineCombination_coe
@@ -480,7 +484,7 @@ theorem weightedVsub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
combinations. -/
@[simp]
theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (w : ι → k)
- (hw : (∑ i in s, w i) = 1) : s.affineCombination p w = ∑ i in s, w i • p i := by
+ (hw : (∑ i in s, w i) = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
simp [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p hw 0]
#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combination
@@ -490,7 +494,7 @@ include S
and has weight 1 and the other points in the set have weight 0. -/
@[simp]
theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i : ι} (his : i ∈ s)
- (hwi : w i = 1) (hw0 : ∀ i2 ∈ s, i2 ≠ i → w i2 = 0) : s.affineCombination p w = p i :=
+ (hwi : w i = 1) (hw0 : ∀ i2 ∈ s, i2 ≠ i → w i2 = 0) : s.affineCombination k p w = p i :=
by
have h1 : (∑ i in s, w i) = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
rw [s.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one w p h1 (p i),
@@ -506,7 +510,8 @@ theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i
/-- An affine combination is unaffected by changing the weights to the
corresponding indicator function and adding points to the set. -/
theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s₂ : Finset ι}
- (h : s₁ ⊆ s₂) : s₁.affineCombination p w = s₂.affineCombination p (Set.indicator (↑s₁) w) := by
+ (h : s₁ ⊆ s₂) : s₁.affineCombination k p w = s₂.affineCombination k p (Set.indicator (↑s₁) w) :=
+ by
rw [affine_combination_apply, affine_combination_apply,
weighted_vsub_of_point_indicator_subset _ _ _ h]
#align finset.affine_combination_indicator_subset Finset.affineCombination_indicator_subset
@@ -515,14 +520,14 @@ theorem affineCombination_indicator_subset (w : ι → k) (p : ι → P) {s₁ s
affine combination with the same points and weights over the original
`finset`. -/
theorem affineCombination_map (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) :
- (s₂.map e).affineCombination p w = s₂.affineCombination (p ∘ e) (w ∘ e) := by
+ (s₂.map e).affineCombination k p w = s₂.affineCombination k (p ∘ e) (w ∘ e) := by
simp_rw [affine_combination_apply, weighted_vsub_of_point_map]
#align finset.affine_combination_map Finset.affineCombination_map
/-- A weighted sum of pairwise subtractions, expressed as a subtraction of two `affine_combination`
expressions. -/
theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι → P) :
- (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.affineCombination p₁ w -ᵥ s.affineCombination p₂ w :=
+ (∑ i in s, w i • (p₁ i -ᵥ p₂ i)) = s.affineCombination k p₁ w -ᵥ s.affineCombination k p₂ w :=
by
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.sum_smul_vsub_eq_weighted_vsub_of_point_sub _ _ _ _
@@ -531,21 +536,21 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.affineCombination p₁ w -ᵥ p₂ :=
+ (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.affineCombination k p₁ w -ᵥ p₂ :=
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = p₁ -ᵥ s.affineCombination p₂ w :=
+ (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = p₁ -ᵥ s.affineCombination k p₂ w :=
by rw [sum_smul_vsub_eq_affine_combination_vsub, affine_combination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
/-- A weighted sum may be split into a subtraction of affine combinations over two subsets. -/
theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s₂ ⊆ s) (w : ι → k)
(p : ι → P) :
- (s \ s₂).affineCombination p w -ᵥ s₂.affineCombination p (-w) = s.weightedVsub p w :=
+ (s \ s₂).affineCombination k p w -ᵥ s₂.affineCombination k p (-w) = s.weightedVsub p w :=
by
simp_rw [affine_combination_apply, vadd_vsub_vadd_cancel_right]
exact s.weighted_vsub_sdiff_sub h _ _
@@ -555,7 +560,7 @@ theorem affineCombination_sdiff_sub [DecidableEq ι] {s₂ : Finset ι} (h : s
the affine combination of the other points with the given weights. -/
theorem affineCombination_eq_of_weightedVsub_eq_zero_of_eq_neg_one {w : ι → k} {p : ι → P}
(hw : s.weightedVsub p w = (0 : V)) {i : ι} [DecidablePred (· ≠ i)] (his : i ∈ s)
- (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination p w = p i := by
+ (hwi : w i = -1) : (s.filterₓ (· ≠ i)).affineCombination k p w = p i := by
classical
rw [← @vsub_eq_zero_iff_eq V, ← hw, ←
s.affine_combination_sdiff_sub (singleton_subset_iff.2 his), sdiff_singleton_eq_erase, ←
@@ -569,8 +574,8 @@ theorem affineCombination_eq_of_weightedVsub_eq_zero_of_eq_neg_one {w : ι → k
/-- An affine combination over `s.subtype pred` equals one over `s.filter pred`. -/
theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred : ι → Prop)
[DecidablePred pred] :
- ((s.Subtype pred).affineCombination (fun i => p i) fun i => w i) =
- (s.filterₓ pred).affineCombination p w :=
+ ((s.Subtype pred).affineCombination k (fun i => p i) fun i => w i) =
+ (s.filterₓ pred).affineCombination k p w :=
by
rw [affine_combination_apply, affine_combination_apply, weighted_vsub_of_point_subtype_eq_filter]
#align finset.affine_combination_subtype_eq_filter Finset.affineCombination_subtype_eq_filter
@@ -579,7 +584,7 @@ theorem affineCombination_subtype_eq_filter (w : ι → k) (p : ι → P) (pred
in `s` not satisfying `pred` are zero. -/
theorem affineCombination_filter_of_ne (w : ι → k) (p : ι → P) {pred : ι → Prop}
[DecidablePred pred] (h : ∀ i ∈ s, w i ≠ 0 → pred i) :
- (s.filterₓ pred).affineCombination p w = s.affineCombination p w := by
+ (s.filterₓ pred).affineCombination k p w = s.affineCombination k p w := by
rw [affine_combination_apply, affine_combination_apply,
s.weighted_vsub_of_point_filter_of_ne _ _ _ h]
#align finset.affine_combination_filter_of_ne Finset.affineCombination_filter_of_ne
@@ -640,9 +645,9 @@ subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
(∃ (fs : Finset ι)(hfs : ↑fs ⊆ s)(w : ι → k)(hw : (∑ i in fs, w i) = 1),
- p0 = fs.affineCombination p w) ↔
+ p0 = fs.affineCombination k p w) ↔
∃ (fs : Finset s)(w : s → k)(hw : (∑ i in fs, w i) = 1),
- p0 = fs.affineCombination (fun i : s => p i) w :=
+ p0 = fs.affineCombination k (fun i : s => p i) w :=
by
simp_rw [affine_combination_apply, eq_vadd_iff_vsub_eq]
exact eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype
@@ -653,7 +658,7 @@ variable {k V}
/-- Affine maps commute with affine combinations. -/
theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.Sum w = 1) (f : P →ᵃ[k] P₂) :
- f (s.affineCombination p w) = s.affineCombination (f ∘ p) w :=
+ f (s.affineCombination k p w) = s.affineCombination k (f ∘ p) w :=
by
have b := Classical.choice (inferInstance : affine_space V P).Nonempty
have b₂ := Classical.choice (inferInstance : affine_space V₂ P₂).Nonempty
@@ -770,7 +775,7 @@ variable (k)
/-- An affine combination with `affine_combination_single_weights` gives the specified point. -/
@[simp]
theorem affineCombination_affineCombinationSingleWeights [DecidableEq ι] (p : ι → P) {i : ι}
- (hi : i ∈ s) : s.affineCombination p (affineCombinationSingleWeights k i) = p i :=
+ (hi : i ∈ s) : s.affineCombination k p (affineCombinationSingleWeights k i) = p i :=
by
refine' s.affine_combination_of_eq_one_of_eq_zero _ _ hi (by simp) _
rintro j - hj
@@ -794,7 +799,7 @@ variable {k}
@[simp]
theorem affineCombination_affineCombinationLineMapWeights [DecidableEq ι] (p : ι → P) {i j : ι}
(hi : i ∈ s) (hj : j ∈ s) (c : k) :
- s.affineCombination p (affineCombinationLineMapWeights i j c) =
+ s.affineCombination k p (affineCombinationLineMapWeights i j c) =
AffineMap.lineMap (p i) (p j) c :=
by
rw [affine_combination_line_map_weights, ← weighted_vsub_vadd_affine_combination,
@@ -862,11 +867,11 @@ include V
is intended to be used in the case where the number of points,
converted to `k`, is not zero. -/
def centroid (p : ι → P) : P :=
- s.affineCombination p (s.centroidWeights k)
+ s.affineCombination k p (s.centroidWeights k)
#align finset.centroid Finset.centroid
/-- The definition of the centroid. -/
-theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination p (s.centroidWeights k) :=
+theorem centroid_def (p : ι → P) : s.centroid k p = s.affineCombination k p (s.centroidWeights k) :=
rfl
#align finset.centroid_def Finset.centroid_def
@@ -973,7 +978,7 @@ include V
/-- The centroid as an affine combination over a `fintype`. -/
theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
- s.centroid k p = univ.affineCombination p (s.centroidWeightsIndicator k) :=
+ s.centroid k p = univ.affineCombination k p (s.centroidWeightsIndicator k) :=
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
@@ -1062,8 +1067,8 @@ theorem weightedVsub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
`affine_span` of an indexed family, if the underlying ring is
nontrivial. -/
theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι → k}
- (h : (∑ i in s, w i) = 1) (p : ι → P) : s.affineCombination p w ∈ affineSpan k (Set.range p) :=
- by
+ (h : (∑ i in s, w i) = 1) (p : ι → P) :
+ s.affineCombination k p w ∈ affineSpan k (Set.range p) := by
classical
have hnz : (∑ i in s, w i) ≠ 0 := h.symm ▸ one_ne_zero
have hn : s.nonempty := Finset.nonempty_of_sum_ne_zero hnz
@@ -1071,15 +1076,15 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
let w1 : ι → k := Function.update (Function.const ι 0) i1 1
have hw1 : (∑ i in s, w1 i) = 1 := by
rw [Finset.sum_update_of_mem hi1, Finset.sum_const_zero, add_zero]
- have hw1s : s.affine_combination p w1 = p i1 :=
+ have hw1s : s.affine_combination k p w1 = p i1 :=
s.affine_combination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
Function.update_noteq hne _ _
- have hv : s.affine_combination p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
+ have hv : s.affine_combination k p w -ᵥ p i1 ∈ (affineSpan k (Set.range p)).direction :=
by
rw [direction_affineSpan, ← hw1s, Finset.affineCombination_vsub]
apply weightedVsub_mem_vectorSpan
simp [Pi.sub_apply, h, hw1]
- rw [← vsub_vadd (s.affine_combination p w) (p i1)]
+ rw [← vsub_vadd (s.affine_combination k p w) (p i1)]
exact AffineSubspace.vadd_mem_of_mem_direction hv (mem_affineSpan k (Set.mem_range_self _))
#align affine_combination_mem_affine_span affineCombination_mem_affineSpan
@@ -1136,7 +1141,7 @@ variable {k}
`eq_affine_combination_of_mem_affine_span_of_fintype`. -/
theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination p w := by
+ ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
@@ -1157,7 +1162,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
let w0 : ι → k := Function.update (Function.const ι 0) i0 1
have hw0 : (∑ i in s', w0 i) = 1 := by
rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero, add_zero]
- have hw0s : s'.affine_combination p w0 = p i0 :=
+ have hw0s : s'.affine_combination k p w0 = p i0 :=
s'.affine_combination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
(Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
use s', w0 + w'
@@ -1168,7 +1173,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k)(hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination p w := by
+ ∃ (w : ι → k)(hw : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
classical
obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
refine'
@@ -1184,7 +1189,7 @@ if it is an `affine_combination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination p w :=
+ ∃ (s : Finset ι)(w : ι → k)(hw : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w :=
by
constructor
· exact eq_affineCombination_of_mem_affineSpan
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -977,7 +977,7 @@ theorem centroid_eq_affineCombination_fintype [Fintype ι] (p : ι → P) :
affineCombination_indicator_subset _ _ (subset_univ _)
#align finset.centroid_eq_affine_combination_fintype Finset.centroid_eq_affineCombination_fintype
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
/-- An indexed family of points that is injective on the given
`finset` has the same centroid as the image of that `finset`. This is
stated in terms of a set equal to the image to provide control of
@@ -1012,8 +1012,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
rw [(hf' x).2]
#align finset.centroid_eq_centroid_image_of_inj_on Finset.centroid_eq_centroid_image_of_inj_on
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i j «expr ∈ » s) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i j «expr ∈ » s₂) -/
/-- Two indexed families of points that are injective on the given
`finset`s and with the same points in the image of those `finset`s
have the same centroid. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240
@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 48765fae5044d8a40aa4c1e485f16b8bd87081af
+! leanprover-community/mathlib commit 87c54600fe3cdc7d32ff5b50873ac724d86aef8d
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Algebra.Invertible
import Mathbin.Algebra.IndicatorFunction
import Mathbin.Algebra.Module.BigOperators
+import Mathbin.Data.Fintype.BigOperators
import Mathbin.LinearAlgebra.AffineSpace.AffineMap
import Mathbin.LinearAlgebra.AffineSpace.AffineSubspace
import Mathbin.LinearAlgebra.Finsupp
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -441,8 +441,8 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
ext
simp
rw [hgf, sum_image]
- simp only [Function.comp_apply]
- exact fun _ _ _ _ hxy => hf hxy
+ · simp only [Function.comp_apply]
+ · exact fun _ _ _ _ hxy => hf hxy
#align finset.attach_affine_combination_of_injective Finset.attach_affineCombination_of_injective
theorem attach_affineCombination_coe (s : Finset P) (w : P → k) :
@@ -432,7 +432,7 @@ theorem affineCombination_vsub (w₁ w₂ : ι → k) (p : ι → P) :
theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w : P → k) (f : s → P)
(hf : Function.Injective f) :
s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w := by
- simp only [affineCombination, weightedVSubOfPoint_apply, id.def, vadd_right_cancel_iff,
+ simp only [affineCombination, weightedVSubOfPoint_apply, id, vadd_right_cancel_iff,
Function.comp_apply, AffineMap.coe_mk]
let g₁ : s → V := fun i => w (f i) • (f i -ᵥ Classical.choice S.nonempty)
let g₂ : P → V := fun i => w i • (i -ᵥ Classical.choice S.nonempty)
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -54,11 +54,8 @@ theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} := by
#align finset.univ_fin2 Finset.univ_fin2
variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
-
variable [S : AffineSpace V P]
-
variable {ι : Type*} (s : Finset ι)
-
variable {ι₂ : Type*} (s₂ : Finset ι₂)
/-- A weighted sum of the results of subtracting a base point from the
@@ -775,7 +772,6 @@ end Finset
namespace Finset
variable (k : Type*) {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
-
variable [AffineSpace V P] {ι : Type*} (s : Finset ι) {ι₂ : Type*} (s₂ : Finset ι₂)
/-- The weights for the centroid of some points. -/
@@ -1194,7 +1190,6 @@ end AffineSpace'
section DivisionRing
variable {k : Type*} {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
-
variable [AffineSpace V P] {ι : Type*}
open Set Finset
@@ -1234,7 +1229,6 @@ end DivisionRing
namespace AffineMap
variable {k : Type*} {V : Type*} (P : Type*) [CommRing k] [AddCommGroup V] [Module k V]
-
variable [AffineSpace V P] {ι : Type*} (s : Finset ι)
-- TODO: define `affineMap.proj`, `affineMap.fst`, `affineMap.snd`
@@ -1002,7 +1002,7 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in
rw [Finsupp.total_apply, Finsupp.onFinset_sum hwx]
· apply Finset.sum_congr rfl
intro i hi
- simp [Set.indicator_apply, if_pos hi]
+ simp [w', Set.indicator_apply, if_pos hi]
· exact fun _ => zero_smul k _
#align weighted_vsub_mem_vector_span weightedVSub_mem_vectorSpan
@@ -1161,7 +1161,7 @@ theorem mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd [Nontrivial k] (p : ι
· simp [Finset.sum_insert hj, Finset.sum_update_of_not_mem hj, hj]
have hww : ∀ i, i ≠ j → w i = w' i := by
intro i hij
- simp [hij]
+ simp [w', hij]
rw [s.weightedVSubOfPoint_eq_of_weights_eq p j w w' hww, ←
s.weightedVSubOfPoint_insert w' p j, ←
(insert j s).affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w' p h₁ (p j)]
Function.const
to the Function
namespace (#10220)
They were in the Pi
namespace instead.
@@ -1018,7 +1018,7 @@ theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι
cases' hn with i1 hi1
let w1 : ι → k := Function.update (Function.const ι 0) i1 1
have hw1 : ∑ i in s, w1 i = 1 := by
- simp only [Pi.const_zero, Finset.sum_update_of_mem hi1, Pi.zero_apply,
+ simp only [Function.const_zero, Finset.sum_update_of_mem hi1, Pi.zero_apply,
Finset.sum_const_zero, add_zero]
have hw1s : s.affineCombination k p w1 = p i1 :=
s.affineCombination_of_eq_one_of_eq_zero w1 p hi1 (Function.update_same _ _ _) fun _ _ hne =>
$
with <|
(#9319)
See Zulip thread for the discussion.
@@ -164,7 +164,7 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
(h : s₁ ⊆ s₂) :
s₁.weightedVSubOfPoint p b w = s₂.weightedVSubOfPoint p b (Set.indicator (↑s₁) w) := by
rw [weightedVSubOfPoint_apply, weightedVSubOfPoint_apply]
- exact Eq.symm $
+ exact Eq.symm <|
sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
@@ -575,9 +575,9 @@ corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V} {x : k} {s : Set ι}
{p : ι → P} {b : P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = x),
+ (∃ fs : Finset ι, ↑fs ⊆ s ∧ ∃ w : ι → k, ∑ i in fs, w i = x ∧
v = fs.weightedVSubOfPoint p b w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = x),
+ ∃ (fs : Finset s) (w : s → k), ∑ i in fs, w i = x ∧
v = fs.weightedVSubOfPoint (fun i : s => p i) b w := by
classical
simp_rw [weightedVSubOfPoint_apply]
@@ -600,9 +600,9 @@ only if it can be expressed as `weightedVSub` with sum of weights 0
for the corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι} {p : ι → P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = 0),
+ (∃ fs : Finset ι, ↑fs ⊆ s ∧ ∃ w : ι → k, ∑ i in fs, w i = 0 ∧
v = fs.weightedVSub p w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = 0),
+ ∃ (fs : Finset s) (w : s → k), ∑ i in fs, w i = 0 ∧
v = fs.weightedVSub (fun i : s => p i) w :=
eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
@@ -618,9 +618,9 @@ indexed family whose index type is the subtype corresponding to that
subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = 1),
+ (∃ fs : Finset ι, ↑fs ⊆ s ∧ ∃ w : ι → k, ∑ i in fs, w i = 1 ∧
p0 = fs.affineCombination k p w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = 1),
+ ∃ (fs : Finset s) (w : s → k), ∑ i in fs, w i = 1 ∧
p0 = fs.affineCombination k (fun i : s => p i) w := by
simp_rw [affineCombination_apply, eq_vadd_iff_vsub_eq]
exact eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
@@ -942,7 +942,7 @@ stated in terms of a set equal to the image to provide control of
definitional equality for the index type used for the centroid of the
image. -/
theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
- (hi : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), p i = p j → i = j) {ps : Set P} [Fintype ps]
+ (hi : ∀ i ∈ s, ∀ j ∈ s, p i = p j → i = j) {ps : Set P} [Fintype ps]
(hps : ps = p '' ↑s) : s.centroid k p = (univ : Finset ps).centroid k fun x => (x : P) := by
let f : p '' ↑s → ι := fun x => x.property.choose
have hf : ∀ x, f x ∈ s ∧ p (f x) = x := fun x => x.property.choose_spec
@@ -972,8 +972,8 @@ theorem centroid_eq_centroid_image_of_inj_on {p : ι → P}
`Finset`s and with the same points in the image of those `Finset`s
have the same centroid. -/
theorem centroid_eq_of_inj_on_of_image_eq {p : ι → P}
- (hi : ∀ (i) (_ : i ∈ s) (j) (_ : j ∈ s), p i = p j → i = j) {p₂ : ι₂ → P}
- (hi₂ : ∀ (i) (_ : i ∈ s₂) (j) (_ : j ∈ s₂), p₂ i = p₂ j → i = j) (he : p '' ↑s = p₂ '' ↑s₂) :
+ (hi : ∀ i ∈ s, ∀ j ∈ s, p i = p j → i = j) {p₂ : ι₂ → P}
+ (hi₂ : ∀ i ∈ s₂, ∀ j ∈ s₂, p₂ i = p₂ j → i = j) (he : p '' ↑s = p₂ '' ↑s₂) :
s.centroid k p = s₂.centroid k p₂ := by
classical rw [s.centroid_eq_centroid_image_of_inj_on k hi rfl,
s₂.centroid_eq_centroid_image_of_inj_on k hi₂ he]
@@ -1040,7 +1040,7 @@ variable (k)
if it is a `weightedVSub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 0), v = s.weightedVSub p w := by
+ ∃ (s : Finset ι) (w : ι → k), ∑ i in s, w i = 0 ∧ v = s.weightedVSub p w := by
classical
constructor
· rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
@@ -1086,7 +1086,7 @@ variable {k}
`eq_affineCombination_of_mem_affineSpan_of_fintype`. -/
theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k), ∑ i in s, w i = 1 ∧ p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
@@ -1111,17 +1111,15 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
have hw0s : s'.affineCombination k p w0 = p i0 :=
s'.affineCombination_of_eq_one_of_eq_zero w0 p (Finset.mem_insert_self _ _)
(Function.update_same _ _ _) fun _ _ hne => Function.update_noteq hne _ _
- use s', w0 + w'
- constructor
- · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
+ refine ⟨s', w0 + w', ?_, ?_⟩
· -- Porting note: proof was `simp [Pi.add_apply, Finset.sum_add_distrib, hw0, h']`
- change (Finset.sum s' fun i => w0 i + w' i) = 1
- simp only [Finset.sum_add_distrib, hw0, h', add_zero]
+ simp only [Pi.add_apply, Finset.sum_add_distrib, hw0, h', add_zero]
+ · rw [add_comm, ← Finset.weightedVSub_vadd_affineCombination, hw0s, hs', vsub_vadd]
#align eq_affine_combination_of_mem_affine_span eq_affineCombination_of_mem_affineSpan
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k) (_ : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
+ ∃ w : ι → k, ∑ i, w i = 1 ∧ p1 = Finset.univ.affineCombination k p w := by
classical
obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
refine'
@@ -1137,7 +1135,7 @@ if it is an `affineCombination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k), ∑ i in s, w i = 1 ∧ p1 = s.affineCombination k p w := by
constructor
· exact eq_affineCombination_of_mem_affineSpan
· rintro ⟨s, w, hw, rfl⟩
cases'
(#9171)
I literally went through and regex'd some uses of cases'
, replacing them with rcases
; this is meant to be a low effort PR as I hope that tools can do this in the future.
rcases
is an easier replacement than cases
, though with better tools we could in future do a second pass converting simple rcases
added here (and existing ones) to cases
.
@@ -102,7 +102,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
simp only [Finset.weightedVSubOfPoint_apply]
congr
ext i
- cases' eq_or_ne i j with h h
+ rcases eq_or_ne i j with h | h
· simp [h]
· simp [hw i h]
#align finset.weighted_vsub_of_point_eq_of_weights_eq Finset.weightedVSubOfPoint_eq_of_weights_eq
Algebra.Support
down the import tree (#8919)
Function.support
is a very basic definition. Nevertheless, it is a pretty heavy import because it imports most objects a support
lemma can be written about.
This PR reverses the dependencies between those objects and Function.support
, so that the latter can become a much more lightweight import.
Only two import could not easily be reversed, namely the ones to Data.Set.Finite
and Order.ConditionallyCompleteLattice.Basic
, so I created two new files instead.
I credit:
@@ -3,7 +3,6 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
-import Mathlib.Algebra.IndicatorFunction
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Data.Fintype.BigOperators
import Mathlib.LinearAlgebra.AffineSpace.AffineMap
@@ -165,8 +164,8 @@ theorem weightedVSubOfPoint_indicator_subset (w : ι → k) (p : ι → P) (b :
(h : s₁ ⊆ s₂) :
s₁.weightedVSubOfPoint p b w = s₂.weightedVSubOfPoint p b (Set.indicator (↑s₁) w) := by
rw [weightedVSubOfPoint_apply, weightedVSubOfPoint_apply]
- exact
- Set.sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
+ exact Eq.symm $
+ sum_indicator_subset_of_eq_zero w (fun i wi => wi • (p i -ᵥ b : V)) h fun i => zero_smul k _
#align finset.weighted_vsub_of_point_indicator_subset Finset.weightedVSubOfPoint_indicator_subset
/-- A weighted sum, over the image of an embedding, equals a weighted
@@ -903,7 +902,7 @@ theorem centroidWeightsIndicator_def :
/-- The sum of the weights for the centroid indexed by a `Fintype`. -/
theorem sum_centroidWeightsIndicator [Fintype ι] :
∑ i, s.centroidWeightsIndicator k i = ∑ i in s, s.centroidWeights k i :=
- (Set.sum_indicator_subset _ (subset_univ _)).symm
+ sum_indicator_subset _ (subset_univ _)
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
/-- In the characteristic zero case, the weights in the centroid
@@ -1100,7 +1099,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
let s' := insert i0 s
let w' := Set.indicator (↑s) w
have h' : ∑ i in s', w' i = 0 := by
- rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
+ rw [← h, Finset.sum_indicator_subset _ (Finset.subset_insert i0 s)]
have hs' : s'.weightedVSub p w' = p1 -ᵥ p i0 := by
rw [hs]
exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
Only Prop
-values fields should be capitalized, not P
-valued fields where P
is Prop
-valued.
Rather than fixing Nonempty :=
in constructors, I just deleted the line as the instance can almost always be found automatically.
@@ -248,7 +248,7 @@ from the given points, as a linear map on the weights. This is
intended to be used when the sum of the weights is 0; that condition
is specified as a hypothesis on those lemmas that require it. -/
def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
- s.weightedVSubOfPoint p (Classical.choice S.Nonempty)
+ s.weightedVSubOfPoint p (Classical.choice S.nonempty)
#align finset.weighted_vsub Finset.weightedVSub
/-- Applying `weightedVSub` with given weights. This is for the case
@@ -258,7 +258,7 @@ that base point will cancel out later); a more typical use case for
`weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero` and then
using `weightedVSubOfPoint_apply`. -/
theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
- s.weightedVSub p w = ∑ i in s, w i • (p i -ᵥ Classical.choice S.Nonempty) := by
+ s.weightedVSub p w = ∑ i in s, w i • (p i -ᵥ Classical.choice S.nonempty) := by
simp [weightedVSub, LinearMap.sum_apply]
#align finset.weighted_vsub_apply Finset.weightedVSub_apply
@@ -371,7 +371,7 @@ points with the given weights; that condition is specified as a
hypothesis on those lemmas that require it. -/
def affineCombination (p : ι → P) : (ι → k) →ᵃ[k] P
where
- toFun w := s.weightedVSubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty
+ toFun w := s.weightedVSubOfPoint p (Classical.choice S.nonempty) w +ᵥ Classical.choice S.nonempty
linear := s.weightedVSub p
map_vadd' w₁ w₂ := by simp_rw [vadd_vadd, weightedVSub, vadd_eq_add, LinearMap.map_add]
#align finset.affine_combination Finset.affineCombination
@@ -395,7 +395,7 @@ point with
then using `weightedVSubOfPoint_apply`. -/
theorem affineCombination_apply (w : ι → k) (p : ι → P) :
(s.affineCombination k p) w =
- s.weightedVSubOfPoint p (Classical.choice S.Nonempty) w +ᵥ Classical.choice S.Nonempty :=
+ s.weightedVSubOfPoint p (Classical.choice S.nonempty) w +ᵥ Classical.choice S.nonempty :=
rfl
#align finset.affine_combination_apply Finset.affineCombination_apply
@@ -438,8 +438,8 @@ theorem attach_affineCombination_of_injective [DecidableEq P] (s : Finset P) (w
s.attach.affineCombination k f (w ∘ f) = (image f univ).affineCombination k id w := by
simp only [affineCombination, weightedVSubOfPoint_apply, id.def, vadd_right_cancel_iff,
Function.comp_apply, AffineMap.coe_mk]
- let g₁ : s → V := fun i => w (f i) • (f i -ᵥ Classical.choice S.Nonempty)
- let g₂ : P → V := fun i => w i • (i -ᵥ Classical.choice S.Nonempty)
+ let g₁ : s → V := fun i => w (f i) • (f i -ᵥ Classical.choice S.nonempty)
+ let g₂ : P → V := fun i => w i • (i -ᵥ Classical.choice S.nonempty)
change univ.sum g₁ = (image f univ).sum g₂
have hgf : g₁ = g₂ ∘ f := by
ext
@@ -633,8 +633,8 @@ variable {k V}
theorem map_affineCombination {V₂ P₂ : Type*} [AddCommGroup V₂] [Module k V₂] [AffineSpace V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.sum w = 1) (f : P →ᵃ[k] P₂) :
f (s.affineCombination k p w) = s.affineCombination k (f ∘ p) w := by
- have b := Classical.choice (inferInstance : AffineSpace V P).Nonempty
- have b₂ := Classical.choice (inferInstance : AffineSpace V₂ P₂).Nonempty
+ have b := Classical.choice (inferInstance : AffineSpace V P).nonempty
+ have b₂ := Classical.choice (inferInstance : AffineSpace V₂ P₂).nonempty
rw [s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w p hw b,
s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w (f ∘ p) hw b₂, ←
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w (f ∘ p) hw (f b) b₂]
_root_.map_sum
more consistently (#7189)
Also _root_.map_smul
when in the neighbourhood.
@@ -639,7 +639,7 @@ theorem map_affineCombination {V₂ P₂ : Type*} [AddCommGroup V₂] [Module k
s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w (f ∘ p) hw b₂, ←
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w (f ∘ p) hw (f b) b₂]
simp only [weightedVSubOfPoint_apply, RingHom.id_apply, AffineMap.map_vadd,
- LinearMap.map_smulₛₗ, AffineMap.linearMap_vsub, LinearMap.map_sum, Function.comp_apply]
+ LinearMap.map_smulₛₗ, AffineMap.linearMap_vsub, map_sum, Function.comp_apply]
#align finset.map_affine_combination Finset.map_affineCombination
variable (k)
@@ -3,7 +3,6 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
-import Mathlib.Algebra.Invertible
import Mathlib.Algebra.IndicatorFunction
import Mathlib.Algebra.Module.BigOperators
import Mathlib.Data.Fintype.BigOperators
In Mathlib/LinearAlgebra/Dual.lean
we also overhaul the universe argument names, as the file switched between two conventions and making up undeclared universe variables.
Mathlib/LinearAlgebra/Prod.lean
invented some new variables even though it already had plenty available.
@@ -43,9 +43,6 @@ These definitions are for sums over a `Finset`; versions for a
-/
-set_option autoImplicit true
-
-
noncomputable section
@@ -988,7 +985,7 @@ end Finset
section AffineSpace'
-variable {k V P : Type*} [Ring k] [AddCommGroup V] [Module k V] [AffineSpace V P]
+variable {ι k V P : Type*} [Ring k] [AddCommGroup V] [Module k V] [AffineSpace V P]
/-- A `weightedVSub` with sum of weights 0 is in the `vectorSpan` of
an indexed family. -/
Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.
The intent of this PR is to make autoImplicit
opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true
in the few files that rely on it.
That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.
I claim that many of the uses of autoImplicit
in these files are accidental; situations such as:
variables
are in scope, but pasting the lemma in the wrong sectionHaving set_option autoImplicit false
as the default prevents these types of mistake being made in the 90% of files where autoImplicit
s are not used at all, and causes them to be caught by CI during review.
I think there were various points during the port where we encouraged porters to delete the universes u v
lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.
A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18
as the no:dontcare:yes
vote ratio.
While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true
has been placed locally within a section, rather than at the top of the file.
@@ -43,6 +43,8 @@ These definitions are for sums over a `Finset`; versions for a
-/
+set_option autoImplicit true
+
noncomputable section
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -56,13 +56,13 @@ theorem univ_fin2 : (univ : Finset (Fin 2)) = {0, 1} := by
fin_cases x <;> simp
#align finset.univ_fin2 Finset.univ_fin2
-variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
variable [S : AffineSpace V P]
-variable {ι : Type _} (s : Finset ι)
+variable {ι : Type*} (s : Finset ι)
-variable {ι₂ : Type _} (s₂ : Finset ι₂)
+variable {ι₂ : Type*} (s₂ : Finset ι₂)
/-- A weighted sum of the results of subtracting a base point from the
given points, as a linear map on the weights. The main cases of
@@ -632,7 +632,7 @@ theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s
variable {k V}
/-- Affine maps commute with affine combinations. -/
-theorem map_affineCombination {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [AffineSpace V₂ P₂]
+theorem map_affineCombination {V₂ P₂ : Type*} [AddCommGroup V₂] [Module k V₂] [AffineSpace V₂ P₂]
(p : ι → P) (w : ι → k) (hw : s.sum w = 1) (f : P →ᵃ[k] P₂) :
f (s.affineCombination k p w) = s.affineCombination k (f ∘ p) w := by
have b := Classical.choice (inferInstance : AffineSpace V P).Nonempty
@@ -777,9 +777,9 @@ end Finset
namespace Finset
-variable (k : Type _) {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
-variable [AffineSpace V P] {ι : Type _} (s : Finset ι) {ι₂ : Type _} (s₂ : Finset ι₂)
+variable [AffineSpace V P] {ι : Type*} (s : Finset ι) {ι₂ : Type*} (s₂ : Finset ι₂)
/-- The weights for the centroid of some points. -/
def centroidWeights : ι → k :=
@@ -986,7 +986,7 @@ end Finset
section AffineSpace'
-variable {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V] [AffineSpace V P]
+variable {k V P : Type*} [Ring k] [AddCommGroup V] [Module k V] [AffineSpace V P]
/-- A `weightedVSub` with sum of weights 0 is in the `vectorSpan` of
an indexed family. -/
@@ -1198,9 +1198,9 @@ end AffineSpace'
section DivisionRing
-variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
-variable [AffineSpace V P] {ι : Type _}
+variable [AffineSpace V P] {ι : Type*}
open Set Finset
@@ -1238,9 +1238,9 @@ end DivisionRing
namespace AffineMap
-variable {k : Type _} {V : Type _} (P : Type _) [CommRing k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} (P : Type*) [CommRing k] [AddCommGroup V] [Module k V]
-variable [AffineSpace V P] {ι : Type _} (s : Finset ι)
+variable [AffineSpace V P] {ι : Type*} (s : Finset ι)
-- TODO: define `affineMap.proj`, `affineMap.fst`, `affineMap.snd`
/-- A weighted sum, as an affine map on the points involved. -/
Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.
This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.
There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.
This was implemented by running Mathlib against a modified Lean that appended _ᾰ
to all automatically generated names, and fixing everything.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -361,7 +361,7 @@ theorem weightedVSub_const_smul (w : ι → k) (p : ι → P) (c : k) :
s.weightedVSubOfPoint_const_smul _ _ _ _
#align finset.weighted_vsub_const_smul Finset.weightedVSub_const_smul
-instance : AffineSpace (ι → k) (ι → k) := Pi.instAddTorsorForAllForAllAddGroup
+instance : AffineSpace (ι → k) (ι → k) := Pi.instAddTorsor
variable (k)
@@ -2,11 +2,6 @@
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Invertible
import Mathlib.Algebra.IndicatorFunction
@@ -17,6 +12,8 @@ import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace
import Mathlib.LinearAlgebra.Finsupp
import Mathlib.Tactic.FinCases
+#align_import linear_algebra.affine_space.combination from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
+
/-!
# Affine combinations of points
∑'
precedence (#5615)
∑
, ∏
and variants).([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤])
replaced by $1 $2 $3
@@ -115,7 +115,7 @@ theorem weightedVSubOfPoint_eq_of_weights_eq (p : ι → P) (j : ι) (w₁ w₂
/-- The weighted sum is independent of the base point when the sum of
the weights is 0. -/
-theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 0)
+theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 0)
(b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w = s.weightedVSubOfPoint p b₂ w := by
apply eq_of_sub_eq_zero
rw [weightedVSubOfPoint_apply, weightedVSubOfPoint_apply, ← sum_sub_distrib]
@@ -129,7 +129,7 @@ theorem weightedVSubOfPoint_eq_of_sum_eq_zero (w : ι → k) (p : ι → P) (h :
/-- The weighted sum, added to the base point, is independent of the
base point when the sum of the weights is 1. -/
-theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : (∑ i in s, w i) = 1)
+theorem weightedVSubOfPoint_vadd_eq_of_sum_eq_one (w : ι → k) (p : ι → P) (h : ∑ i in s, w i = 1)
(b₁ b₂ : P) : s.weightedVSubOfPoint p b₁ w +ᵥ b₁ = s.weightedVSubOfPoint p b₂ w +ᵥ b₂ := by
erw [weightedVSubOfPoint_apply, weightedVSubOfPoint_apply, ← @vsub_eq_zero_iff_eq V,
vadd_vsub_assoc, vsub_vadd_eq_vsub_sub, ← add_sub_assoc, add_comm, add_sub_assoc, ←
@@ -270,14 +270,14 @@ theorem weightedVSub_apply (w : ι → k) (p : ι → P) :
/-- `weightedVSub` gives the sum of the results of subtracting any
base point, when the sum of the weights is 0. -/
theorem weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero (w : ι → k) (p : ι → P)
- (h : (∑ i in s, w i) = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
+ (h : ∑ i in s, w i = 0) (b : P) : s.weightedVSub p w = s.weightedVSubOfPoint p b w :=
s.weightedVSubOfPoint_eq_of_sum_eq_zero w p h _ _
#align finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero
/-- The value of `weightedVSub`, where the given points are equal and the sum of the weights
is 0. -/
@[simp]
-theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 0) :
+theorem weightedVSub_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 0) :
s.weightedVSub (fun _ => p) w = 0 := by
rw [weightedVSub, weightedVSubOfPoint_apply_const, h, zero_smul]
#align finset.weighted_vsub_apply_const Finset.weightedVSub_apply_const
@@ -320,14 +320,14 @@ theorem sum_smul_vsub_eq_weightedVSub_sub (w : ι → k) (p₁ p₂ : ι → P)
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 0. -/
theorem sum_smul_vsub_const_eq_weightedVSub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSub p₁ w := by
+ (h : ∑ i in s, w i = 0) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.weightedVSub p₁ w := by
rw [sum_smul_vsub_eq_weightedVSub_sub, s.weightedVSub_apply_const _ _ h, sub_zero]
#align finset.sum_smul_vsub_const_eq_weighted_vsub Finset.sum_smul_vsub_const_eq_weightedVSub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 0. -/
theorem sum_smul_const_vsub_eq_neg_weightedVSub (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 0) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = -s.weightedVSub p₂ w := by
+ (h : ∑ i in s, w i = 0) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = -s.weightedVSub p₂ w := by
rw [sum_smul_vsub_eq_weightedVSub_sub, s.weightedVSub_apply_const _ _ h, zero_sub]
#align finset.sum_smul_const_vsub_eq_neg_weighted_vsub Finset.sum_smul_const_vsub_eq_neg_weightedVSub
@@ -406,7 +406,7 @@ theorem affineCombination_apply (w : ι → k) (p : ι → P) :
/-- The value of `affineCombination`, where the given points are equal. -/
@[simp]
-theorem affineCombination_apply_const (w : ι → k) (p : P) (h : (∑ i in s, w i) = 1) :
+theorem affineCombination_apply_const (w : ι → k) (p : P) (h : ∑ i in s, w i = 1) :
s.affineCombination k (fun _ => p) w = p := by
rw [affineCombination_apply, s.weightedVSubOfPoint_apply_const, h, one_smul, vsub_vadd]
#align finset.affine_combination_apply_const Finset.affineCombination_apply_const
@@ -421,7 +421,7 @@ theorem affineCombination_congr {w₁ w₂ : ι → k} (hw : ∀ i ∈ s, w₁ i
/-- `affineCombination` gives the sum with any base point, when the
sum of the weights is 1. -/
theorem affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one (w : ι → k) (p : ι → P)
- (h : (∑ i in s, w i) = 1) (b : P) :
+ (h : ∑ i in s, w i = 1) (b : P) :
s.affineCombination k p w = s.weightedVSubOfPoint p b w +ᵥ b :=
s.weightedVSubOfPoint_vadd_eq_of_sum_eq_one w p h _ _
#align finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one
@@ -472,7 +472,7 @@ theorem weightedVSub_eq_linear_combination {ι} (s : Finset ι) {w : ι → k} {
combinations. -/
@[simp]
theorem affineCombination_eq_linear_combination (s : Finset ι) (p : ι → V) (w : ι → k)
- (hw : (∑ i in s, w i) = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
+ (hw : ∑ i in s, w i = 1) : s.affineCombination k p w = ∑ i in s, w i • p i := by
simp [s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w p hw 0]
#align finset.affine_combination_eq_linear_combination Finset.affineCombination_eq_linear_combination
@@ -481,7 +481,7 @@ and has weight 1 and the other points in the set have weight 0. -/
@[simp]
theorem affineCombination_of_eq_one_of_eq_zero (w : ι → k) (p : ι → P) {i : ι} (his : i ∈ s)
(hwi : w i = 1) (hw0 : ∀ i2 ∈ s, i2 ≠ i → w i2 = 0) : s.affineCombination k p w = p i := by
- have h1 : (∑ i in s, w i) = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
+ have h1 : ∑ i in s, w i = 1 := hwi ▸ sum_eq_single i hw0 fun h => False.elim (h his)
rw [s.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one w p h1 (p i),
weightedVSubOfPoint_apply]
convert zero_vadd V (p i)
@@ -521,14 +521,14 @@ theorem sum_smul_vsub_eq_affineCombination_vsub (w : ι → k) (p₁ p₂ : ι
/-- A weighted sum of pairwise subtractions, where the point on the right is constant and the
sum of the weights is 1. -/
theorem sum_smul_vsub_const_eq_affineCombination_vsub (w : ι → k) (p₁ : ι → P) (p₂ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.affineCombination k p₁ w -ᵥ p₂ :=
+ (h : ∑ i in s, w i = 1) : (∑ i in s, w i • (p₁ i -ᵥ p₂)) = s.affineCombination k p₁ w -ᵥ p₂ :=
by rw [sum_smul_vsub_eq_affineCombination_vsub, affineCombination_apply_const _ _ _ h]
#align finset.sum_smul_vsub_const_eq_affine_combination_vsub Finset.sum_smul_vsub_const_eq_affineCombination_vsub
/-- A weighted sum of pairwise subtractions, where the point on the left is constant and the
sum of the weights is 1. -/
theorem sum_smul_const_vsub_eq_vsub_affineCombination (w : ι → k) (p₂ : ι → P) (p₁ : P)
- (h : (∑ i in s, w i) = 1) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = p₁ -ᵥ s.affineCombination k p₂ w :=
+ (h : ∑ i in s, w i = 1) : (∑ i in s, w i • (p₁ -ᵥ p₂ i)) = p₁ -ᵥ s.affineCombination k p₂ w :=
by rw [sum_smul_vsub_eq_affineCombination_vsub, affineCombination_apply_const _ _ _ h]
#align finset.sum_smul_const_vsub_eq_vsub_affine_combination Finset.sum_smul_const_vsub_eq_vsub_affineCombination
@@ -581,9 +581,9 @@ corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype {v : V} {x : k} {s : Set ι}
{p : ι → P} {b : P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : (∑ i in fs, w i) = x),
+ (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint p b w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : (∑ i in fs, w i) = x),
+ ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = x),
v = fs.weightedVSubOfPoint (fun i : s => p i) b w := by
classical
simp_rw [weightedVSubOfPoint_apply]
@@ -606,9 +606,9 @@ only if it can be expressed as `weightedVSub` with sum of weights 0
for the corresponding indexed family whose index type is the subtype
corresponding to that subset. -/
theorem eq_weightedVSub_subset_iff_eq_weightedVSub_subtype {v : V} {s : Set ι} {p : ι → P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : (∑ i in fs, w i) = 0),
+ (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = 0),
v = fs.weightedVSub p w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : (∑ i in fs, w i) = 0),
+ ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = 0),
v = fs.weightedVSub (fun i : s => p i) w :=
eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
#align finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype
@@ -624,9 +624,9 @@ indexed family whose index type is the subtype corresponding to that
subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
- (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : (∑ i in fs, w i) = 1),
+ (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : ∑ i in fs, w i = 1),
p0 = fs.affineCombination k p w) ↔
- ∃ (fs : Finset s) (w : s → k) (_ : (∑ i in fs, w i) = 1),
+ ∃ (fs : Finset s) (w : s → k) (_ : ∑ i in fs, w i = 1),
p0 = fs.affineCombination k (fun i : s => p i) w := by
simp_rw [affineCombination_apply, eq_vadd_iff_vsub_eq]
exact eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
@@ -666,7 +666,7 @@ theorem affineCombinationSingleWeights_apply_of_ne [DecidableEq ι] {i j : ι} (
@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
- (∑ j in s, affineCombinationSingleWeights k i j) = 1 := by
+ ∑ j in s, affineCombinationSingleWeights k i j = 1 := by
rw [← affineCombinationSingleWeights_apply_self k i]
exact sum_eq_single_of_mem i h fun j _ hj => affineCombinationSingleWeights_apply_of_ne k hj
#align finset.sum_affine_combination_single_weights Finset.sum_affineCombinationSingleWeights
@@ -698,7 +698,7 @@ theorem weightedVSubVSubWeights_apply_of_ne [DecidableEq ι] {i j t : ι} (hi :
@[simp]
theorem sum_weightedVSubVSubWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s) :
- (∑ t in s, weightedVSubVSubWeights k i j t) = 0 := by
+ ∑ t in s, weightedVSubVSubWeights k i j t = 0 := by
simp_rw [weightedVSubVSubWeights, Pi.sub_apply, sum_sub_distrib]
simp [hi, hj]
#align finset.sum_weighted_vsub_vsub_weights Finset.sum_weightedVSubVSubWeights
@@ -736,7 +736,7 @@ theorem affineCombinationLineMapWeights_apply_of_ne [DecidableEq ι] {i j t : ι
@[simp]
theorem sum_affineCombinationLineMapWeights [DecidableEq ι] {i j : ι} (hi : i ∈ s) (hj : j ∈ s)
- (c : k) : (∑ t in s, affineCombinationLineMapWeights i j c t) = 1 := by
+ (c : k) : ∑ t in s, affineCombinationLineMapWeights i j c t = 1 := by
simp_rw [affineCombinationLineMapWeights, Pi.add_apply, sum_add_distrib]
simp [hi, hj, ← mul_sum]
#align finset.sum_affine_combination_line_map_weights Finset.sum_affineCombinationLineMapWeights
@@ -805,7 +805,7 @@ variable {k}
/-- The weights in the centroid sum to 1, if the number of points,
converted to `k`, is not zero. -/
theorem sum_centroidWeights_eq_one_of_cast_card_ne_zero (h : (card s : k) ≠ 0) :
- (∑ i in s, s.centroidWeights k i) = 1 := by simp [h]
+ ∑ i in s, s.centroidWeights k i = 1 := by simp [h]
#align finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero
variable (k)
@@ -813,7 +813,7 @@ variable (k)
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is not zero. -/
theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠ 0) :
- (∑ i in s, s.centroidWeights k i) = 1 := by
+ ∑ i in s, s.centroidWeights k i = 1 := by
-- Porting note: `simp` cannot find `mul_inv_cancel` and does not use `norm_cast`
simp only [centroidWeights_apply, sum_const, nsmul_eq_mul, ne_eq, Nat.cast_eq_zero, card_eq_zero]
refine mul_inv_cancel ?_
@@ -823,14 +823,14 @@ theorem sum_centroidWeights_eq_one_of_card_ne_zero [CharZero k] (h : card s ≠
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the set is nonempty. -/
theorem sum_centroidWeights_eq_one_of_nonempty [CharZero k] (h : s.Nonempty) :
- (∑ i in s, s.centroidWeights k i) = 1 :=
+ ∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (ne_of_gt (card_pos.2 h))
#align finset.sum_centroid_weights_eq_one_of_nonempty Finset.sum_centroidWeights_eq_one_of_nonempty
/-- In the characteristic zero case, the weights in the centroid sum
to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeights_eq_one_of_card_eq_add_one [CharZero k] {n : ℕ} (h : card s = n + 1) :
- (∑ i in s, s.centroidWeights k i) = 1 :=
+ ∑ i in s, s.centroidWeights k i = 1 :=
s.sum_centroidWeights_eq_one_of_card_ne_zero k (h.symm ▸ Nat.succ_ne_zero n)
#align finset.sum_centroid_weights_eq_one_of_card_eq_add_one Finset.sum_centroidWeights_eq_one_of_card_eq_add_one
@@ -907,7 +907,7 @@ theorem centroidWeightsIndicator_def :
/-- The sum of the weights for the centroid indexed by a `Fintype`. -/
theorem sum_centroidWeightsIndicator [Fintype ι] :
- (∑ i, s.centroidWeightsIndicator k i) = ∑ i in s, s.centroidWeights k i :=
+ ∑ i, s.centroidWeightsIndicator k i = ∑ i in s, s.centroidWeights k i :=
(Set.sum_indicator_subset _ (subset_univ _)).symm
#align finset.sum_centroid_weights_indicator Finset.sum_centroidWeightsIndicator
@@ -915,7 +915,7 @@ theorem sum_centroidWeightsIndicator [Fintype ι] :
indexed by a `Fintype` sum to 1 if the number of points is not
zero. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintype ι]
- (h : card s ≠ 0) : (∑ i, s.centroidWeightsIndicator k i) = 1 := by
+ (h : card s ≠ 0) : ∑ i, s.centroidWeightsIndicator k i = 1 := by
rw [sum_centroidWeightsIndicator]
exact s.sum_centroidWeights_eq_one_of_card_ne_zero k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_ne_zero Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero
@@ -923,7 +923,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_card_ne_zero [CharZero k] [Fintyp
/-- In the characteristic zero case, the weights in the centroid
indexed by a `Fintype` sum to 1 if the set is nonempty. -/
theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι] (h : s.Nonempty) :
- (∑ i, s.centroidWeightsIndicator k i) = 1 := by
+ ∑ i, s.centroidWeightsIndicator k i = 1 := by
rw [sum_centroidWeightsIndicator]
exact s.sum_centroidWeights_eq_one_of_nonempty k h
#align finset.sum_centroid_weights_indicator_eq_one_of_nonempty Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty
@@ -931,7 +931,7 @@ theorem sum_centroidWeightsIndicator_eq_one_of_nonempty [CharZero k] [Fintype ι
/-- In the characteristic zero case, the weights in the centroid
indexed by a `Fintype` sum to 1 if the number of points is `n + 1`. -/
theorem sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one [CharZero k] [Fintype ι] {n : ℕ}
- (h : card s = n + 1) : (∑ i, s.centroidWeightsIndicator k i) = 1 := by
+ (h : card s = n + 1) : ∑ i, s.centroidWeightsIndicator k i = 1 := by
rw [sum_centroidWeightsIndicator]
exact s.sum_centroidWeights_eq_one_of_card_eq_add_one k h
#align finset.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one
@@ -993,7 +993,7 @@ variable {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V] [AffineSpace V
/-- A `weightedVSub` with sum of weights 0 is in the `vectorSpan` of
an indexed family. -/
-theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i in s, w i) = 0)
+theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : ∑ i in s, w i = 0)
(p : ι → P) : s.weightedVSub p w ∈ vectorSpan k (Set.range p) := by
classical
rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
@@ -1016,14 +1016,14 @@ theorem weightedVSub_mem_vectorSpan {s : Finset ι} {w : ι → k} (h : (∑ i i
`affineSpan` of an indexed family, if the underlying ring is
nontrivial. -/
theorem affineCombination_mem_affineSpan [Nontrivial k] {s : Finset ι} {w : ι → k}
- (h : (∑ i in s, w i) = 1) (p : ι → P) :
+ (h : ∑ i in s, w i = 1) (p : ι → P) :
s.affineCombination k p w ∈ affineSpan k (Set.range p) := by
classical
- have hnz : (∑ i in s, w i) ≠ 0 := h.symm ▸ one_ne_zero
+ have hnz : ∑ i in s, w i ≠ 0 := h.symm ▸ one_ne_zero
have hn : s.Nonempty := Finset.nonempty_of_sum_ne_zero hnz
cases' hn with i1 hi1
let w1 : ι → k := Function.update (Function.const ι 0) i1 1
- have hw1 : (∑ i in s, w1 i) = 1 := by
+ have hw1 : ∑ i in s, w1 i = 1 := by
simp only [Pi.const_zero, Finset.sum_update_of_mem hi1, Pi.zero_apply,
Finset.sum_const_zero, add_zero]
have hw1s : s.affineCombination k p w1 = p i1 :=
@@ -1046,7 +1046,7 @@ variable (k)
if it is a `weightedVSub` with sum of weights 0. -/
theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
v ∈ vectorSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (_ : (∑ i in s, w i) = 0), v = s.weightedVSub p w := by
+ ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 0), v = s.weightedVSub p w := by
classical
constructor
· rcases isEmpty_or_nonempty ι with (hι | ⟨⟨i0⟩⟩)
@@ -1059,7 +1059,7 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
(l : ι → k) - Function.update (Function.const ι 0 : ι → k) i0 (∑ i in l.support, l i) with
hwdef
use w
- have hw : (∑ i in insert i0 l.support, w i) = 0 := by
+ have hw : ∑ i in insert i0 l.support, w i = 0 := by
rw [hwdef]
simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
Finset.sum_update_of_mem (Finset.mem_insert_self _ _),
@@ -1092,7 +1092,7 @@ variable {k}
`eq_affineCombination_of_mem_affineSpan_of_fintype`. -/
theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (s : Finset ι) (w : ι → k) (_ : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
classical
have hn : (affineSpan k (Set.range p) : Set P).Nonempty := ⟨p1, h⟩
rw [affineSpan_nonempty, Set.range_nonempty_iff_nonempty] at hn
@@ -1104,13 +1104,13 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
rcases hd with ⟨s, w, h, hs⟩
let s' := insert i0 s
let w' := Set.indicator (↑s) w
- have h' : (∑ i in s', w' i) = 0 := by
+ have h' : ∑ i in s', w' i = 0 := by
rw [← h, Set.sum_indicator_subset _ (Finset.subset_insert i0 s)]
have hs' : s'.weightedVSub p w' = p1 -ᵥ p i0 := by
rw [hs]
exact (Finset.weightedVSub_indicator_subset _ _ (Finset.subset_insert i0 s)).symm
let w0 : ι → k := Function.update (Function.const ι 0) i0 1
- have hw0 : (∑ i in s', w0 i) = 1 := by
+ have hw0 : ∑ i in s', w0 i = 1 := by
rw [Finset.sum_update_of_mem (Finset.mem_insert_self _ _)]
simp only [Finset.mem_insert, true_or, not_true, Function.const_apply, Finset.sum_const_zero,
add_zero]
@@ -1127,7 +1127,7 @@ theorem eq_affineCombination_of_mem_affineSpan {p1 : P} {p : ι → P}
theorem eq_affineCombination_of_mem_affineSpan_of_fintype [Fintype ι] {p1 : P} {p : ι → P}
(h : p1 ∈ affineSpan k (Set.range p)) :
- ∃ (w : ι → k) (_ : (∑ i, w i) = 1), p1 = Finset.univ.affineCombination k p w := by
+ ∃ (w : ι → k) (_ : ∑ i, w i = 1), p1 = Finset.univ.affineCombination k p w := by
classical
obtain ⟨s, w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan h
refine'
@@ -1143,7 +1143,7 @@ if it is an `affineCombination` with sum of weights 1, provided the
underlying ring is nontrivial. -/
theorem mem_affineSpan_iff_eq_affineCombination [Nontrivial k] {p1 : P} {p : ι → P} :
p1 ∈ affineSpan k (Set.range p) ↔
- ∃ (s : Finset ι) (w : ι → k) (_ : (∑ i in s, w i) = 1), p1 = s.affineCombination k p w := by
+ ∃ (s : Finset ι) (w : ι → k) (_ : ∑ i in s, w i = 1), p1 = s.affineCombination k p w := by
constructor
· exact eq_affineCombination_of_mem_affineSpan
· rintro ⟨s, w, hw, rfl⟩
@@ -624,9 +624,9 @@ indexed family whose index type is the subtype corresponding to that
subset. -/
theorem eq_affineCombination_subset_iff_eq_affineCombination_subtype {p0 : P} {s : Set ι}
{p : ι → P} :
- (∃ (fs : Finset ι)(_ : ↑fs ⊆ s)(w : ι → k)(_ : (∑ i in fs, w i) = 1),
+ (∃ (fs : Finset ι) (_ : ↑fs ⊆ s) (w : ι → k) (_ : (∑ i in fs, w i) = 1),
p0 = fs.affineCombination k p w) ↔
- ∃ (fs : Finset s)(w : s → k)(_ : (∑ i in fs, w i) = 1),
+ ∃ (fs : Finset s) (w : s → k) (_ : (∑ i in fs, w i) = 1),
p0 = fs.affineCombination k (fun i : s => p i) w := by
simp_rw [affineCombination_apply, eq_vadd_iff_vsub_eq]
exact eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype
fix-comments.py
on all files.@@ -884,7 +884,7 @@ theorem centroid_pair_fin [Invertible (2 : k)] (p : Fin 2 → P) :
#align finset.centroid_pair_fin Finset.centroid_pair_fin
/-- A centroid, over the image of an embedding, equals a centroid with
-the same points and weights over the original `finset`. -/
+the same points and weights over the original `Finset`. -/
theorem centroid_map (e : ι₂ ↪ ι) (p : ι → P) : (s₂.map e).centroid k p = s₂.centroid k (p ∘ e) :=
by simp [centroid_def, affineCombination_map, centroidWeights]
#align finset.centroid_map Finset.centroid_map
The main breaking change is that tac <;> [t1, t2]
is now written tac <;> [t1; t2]
, to avoid clashing with tactics like cases
and use
that take comma-separated lists.
@@ -1193,7 +1193,7 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
<;> erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq ⊢
<;> obtain ⟨t, μ, rfl⟩ := hq
<;> use t
- <;> [(use fun x => μ x * ↑(w x)), (use fun x => μ x * ↑(w x)⁻¹)]
+ <;> [use fun x => μ x * ↑(w x); use fun x => μ x * ↑(w x)⁻¹]
<;> simp [smul_smul]
#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_units
Now that leanprover/lean4#2210 has been merged, this PR:
set_option synthInstance.etaExperiment true
commands (and some etaExperiment%
term elaborators)set_option maxHeartbeats
commandsCo-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>
@@ -47,7 +47,6 @@ These definitions are for sums over a `Finset`; versions for a
-/
-set_option synthInstance.etaExperiment true -- Porting note: gets around lean4#2074
noncomputable section
closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986
@@ -1063,9 +1063,8 @@ theorem mem_vectorSpan_iff_eq_weightedVSub {v : V} {p : ι → P} :
have hw : (∑ i in insert i0 l.support, w i) = 0 := by
rw [hwdef]
simp_rw [Pi.sub_apply, Finset.sum_sub_distrib,
- Finset.sum_update_of_mem (Finset.mem_insert_self _ _), Finset.sum_const_zero,
- Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1, add_zero,
- sub_self]
+ Finset.sum_update_of_mem (Finset.mem_insert_self _ _),
+ Finset.sum_insert_of_eq_zero_if_not_mem Finsupp.not_mem_support_iff.1]
simp only [Finsupp.mem_support_iff, ne_eq, Finset.mem_insert, true_or, not_true,
Function.const_apply, Finset.sum_const_zero, add_zero, sub_self]
use hw
@@ -1195,14 +1195,8 @@ theorem affineSpan_eq_affineSpan_lineMap_units [Nontrivial k] {s : Set P} {p : P
<;> erw [mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd k V _ (⟨p, hp⟩ : s) q] at hq ⊢
<;> obtain ⟨t, μ, rfl⟩ := hq
<;> use t
- -- Porting note: remaining proof was:
- --<;> [use fun x => μ x * ↑(w x), use fun x => μ x * ↑(w x)⁻¹]
- --<;> simp [smul_smul]
- -- but this fails with `no enough tactics` error
- { use fun x => μ x * ↑(w x)
- simp [smul_smul] }
- { use fun x => μ x * ↑(w x)⁻¹
- simp [smul_smul] }
+ <;> [(use fun x => μ x * ↑(w x)), (use fun x => μ x * ↑(w x)⁻¹)]
+ <;> simp [smul_smul]
#align affine_span_eq_affine_span_line_map_units affineSpan_eq_affineSpan_lineMap_units
end AffineSpace'
@@ -1255,27 +1249,15 @@ variable [AffineSpace V P] {ι : Type _} (s : Finset ι)
-- TODO: define `affineMap.proj`, `affineMap.fst`, `affineMap.snd`
/-- A weighted sum, as an affine map on the points involved. -/
-def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V
- where
+def weightedVSubOfPoint (w : ι → k) : (ι → P) × P →ᵃ[k] V where
toFun p := s.weightedVSubOfPoint p.fst p.snd w
linear := ∑ i in s, w i • ((LinearMap.proj i).comp (LinearMap.fst _ _ _) - LinearMap.snd _ _ _)
map_vadd' := by
rintro ⟨p, b⟩ ⟨v, b'⟩
- simp only [Finset.weightedVSubOfPoint_apply, LinearMap.coeFn_sum, Finset.sum_apply,
- LinearMap.smul_apply, LinearMap.sub_apply, LinearMap.coe_comp, LinearMap.coe_proj,
- Function.eval, Function.comp_apply, LinearMap.fst_apply, LinearMap.snd_apply, vadd_eq_add]
- rw [← Finset.sum_add_distrib]
- refine Finset.sum_congr rfl (fun x _ => ?_)
- rw [← smul_add]
- congr
- -- Porting note: `simp` fails to simplify `Prod.fst` and `Prod.snd`
- change (v +ᵥ p) x -ᵥ (b' +ᵥ b) = _
- rw [Pi.vadd_apply', sub_add_eq_add_sub, vsub_vadd_eq_vsub_sub, vadd_vsub_assoc]
- -- Porting note proof was:
- --rintro ⟨p, b⟩ ⟨v, b'⟩
- --simp only [LinearMap.sum_apply, Finset.weightedVSubOfPoint, vsub_vadd_eq_vsub_sub,
- -- vadd_vsub_assoc,
- -- add_sub, ← sub_add_eq_add_sub, smul_add, Finset.sum_add_distrib]
+ -- Porting note: needed to give `Prod.mk_vadd_mk` a hint
+ simp [LinearMap.sum_apply, Finset.weightedVSubOfPoint, vsub_vadd_eq_vsub_sub,
+ vadd_vsub_assoc,
+ add_sub, ← sub_add_eq_add_sub, smul_add, Finset.sum_add_distrib, Prod.mk_vadd_mk v]
#align affine_map.weighted_vsub_of_point AffineMap.weightedVSubOfPoint
end AffineMap
The hash was out of date due to a fix in the mathlib3 file, which was needed for porting.
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
! This file was ported from Lean 3 source module linear_algebra.affine_space.combination
-! leanprover-community/mathlib commit 87c54600fe3cdc7d32ff5b50873ac724d86aef8d
+! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
The unported dependencies are